Learning Center
Plans & pricing Sign in
Sign Out

Teori Quantum

VIEWS: 448 PAGES: 15

									                      "In the year nineteen hundred, in the course of purely

                      theoretical (mathematical) investigation, Max Planck

                      made a very remarkable discovery: the law of

                      radiation of bodies as a function of temperature could

                      not be derived solely from the Laws of Maxwellian

 electrodynamics. To arrive at results consistent with the relevant

 experiments, radiation of a given frequency f had to be treated as though it

 consisted of energy atoms (photons) of the individual energy hf, where h is

 Planck's universal constant. During the years following, it was shown that

 light was everywhere produced and absorbed in such energy quanta. In

 particular, Niels Bohr was able to largely understand the structure of the

 atom, on the assumption that the atoms can only have discrete energy

 values, and that the discontinuous transitions between them are connected

 with the emission or absorption of energy quantum. This threw some light

 on the fact that in their gaseous state elements and their compounds

 radiate and absorb only light of certain sharply defined frequencies." (Albert

 Einstein, 1940)

 Quantum Theory: Albert Einstein

 Albert Einstein on Plank's Discovery of Quantum Properties of Light

 In 1900 Max Planck made a profound discovery. He showed (from purely

Fisika Kuantum                                                                    1
 formal/mathematical foundations) that light energy must be emitted and

 absorbed in discrete amounts if it was to correctly describe observed

 phenomena (i.e. Blackbody radiation). Prior to then light had been

 considered as a continuous electromagnetic wave, thus the discrete nature

 of light was completely unexpected, as Albert Einstein explains; About

 fifteen years ago [1899] nobody had yet doubted that a correct account of

 the electrical, optical, and thermal properties of matter was possible on the

 basis of Galileo-Newtonian mechanics applied to molecular motion and of

 Maxwell's theory of the electromagnetic field. (Albert Einstein, 1915) Then

 Planck showed that in order to establish a law of heat radiation (Infra red

 light waves) consonant with experience, it was necessary to employ a

 method of calculation whose incompatibility with the principles of classical

 physics became clearer and clearer. For with this method of calculation,

 Planck introduced into physics the quantum hypothesis, which has since

 received brilliant confirmation. (Albert Einstein, 1914) Albert Einstein (1905)

 used Planck's relationship to explain the results of the photoelectric effect

 which showed that the energy E of ejected electrons was wholly dependent

 upon the frequency f of incident light as described in the equation E=hf. It is

 ironic that in 1921 Albert Einstein was awarded the Nobel Prize for this

 discovery, though he never believed in particles and acknowledged that he

 did not know the cause of the discrete energy transfers (photons) which

Fisika Kuantum                                                                     2
 were contradictory to his continuous field theory of matter.

 In 1954 Albert Einstein wrote to his friend Michael Besso expressing his


 All these fifty years of conscious brooding have brought me no nearer to

 the answer to the question, 'What are light quanta?' Nowadays every Tom,

 Dick and Harry thinks he knows it, but he is mistaken. (Albert Einstein,

 1954) Most importantly, Albert Einstein also suspected that Matter could

 not be described by a continuous spherical force field;

 I consider it quite possible that physics cannot be based on the field

 concept, i.e., on continuous structures. In that case, nothing remains of my

 entire castle in the air, gravitation theory included, [and of] the rest of

 modern physics. (Albert Einstein, 1954) Albert Einstein's suspicions were

 well justified, for he had spent a lifetime trying (and failing) to create a

 unified field theory of matter that explained both Quantum Theory / Light

 and Relativity / Gravity. However, his work on the photoelectric effect

 confirmed that light energy was emitted and absorbed by electrons in

 discrete amounts or quanta. This quanta of light energy soon became

 known as the 'photon' (i.e. discrete like a particle) and led to the paradox

 that light behaved both as a continuous e-m wave (Maxwell, Albert

 Einstein) as well as a discrete particle/photon (Planck, Albert Einstein). So

 we see that Albert Einstein was partly responsible for the discovery of the

Fisika Kuantum                                                                   3
 particle/photon concept of light, though he completely rejected the notion of

 discrete particles. He writes; Since the theory of general relativity implies

 the representation of physical reality by a continuous field, the concept of

 particles or material points cannot play a fundamental part, nor can the

 concept of motion. (Albert Einstein) I wished to show that space time is not

 necessarily something to which one can ascribe to a separate existence,

 independently of the actual objects of physical reality. Physical objects are

 not in space, but these objects are spatially extended. In this way the

 concept empty space loses its meaning. (Albert Einstein)

 Quantum Theory: Louis de Broglie

 de Broglie's Discovery of the Wave Properties of Electron Interactions

 (1927) The next step was taken by de Broglie. He asked himself how the

 discrete states could be understood by the aid of current concepts, and hit

 on a parallel with stationary (standing) waves, as for instance in the case of

 proper frequencies of organ pipes and strings in acoustics. Albert Einstein,

 1954) de Broglie's realisation that standing waves exist at discrete

 frequencies and thus energies is obviously true and important, yet he also

 continued with the particle concept and thus imagined particles moving in a

 wavelike manner. These predicted wave properties of matter were shortly

 thereafter confirmed from experiments (Davisson and Germer, 1927) on

Fisika Kuantum                                                                    4
 the scattering of electrons through crystals (which act as diffraction slits).

 As Albert Einstein confirms;

 Experiments on interference made with particle rays have given brilliant

 proof that the wave character of the phenomena of motion as assumed by

 the theory does, really, correspond to the facts. (Albert Einstein, 1954)

 In 1913, Niels Bohr had developed a simple (though only partly correct)

 model for the hydrogen atom that assumed;

 i) That the electron particle moves in circular orbits about the proton


 ii) Only certain orbits are stable / allowed.

 iii) Light is emitted and absorbed by the atom when the electron 'jumps'

 from one allowed orbital state to a another.

 This early atomic model had some limited success because it was

 obviously created to explain the discrete energy states of light emitted and

 absorbed by bound electrons in atoms or molecules, as discovered by

 Planck in 1900. de Broglie was aware of Bohr's model for the atom and he

 cleverly found a way of explaining why only certain orbits were 'allowed' for

 the electron. As Albert Einstein explains; de Broglie conceived an electron

 revolving about the atomic nucleus as being connected with a hypothetical

 wave train, and made intelligible to some extent the discrete character of

 Bohr's 'permitted' paths by the stationary (standing) character of the

Fisika Kuantum                                                                    5
 corresponding waves. (Albert Einstein, 1940)

 Fig: 1. The allowed discrete orbits of the electron as imagined by de


 de Broglie assumed that because light had both particle and wave

 properties, that this may also be true for matter. Thus he was not actually

 looking for a wave structure of matter. Instead, as matter was already

 assumed to be a particle, he was looking for wave properties of matter to

 complement the known particle properties. As a consequence of this

 particle/wave duality, de Broglie imagined the standing waves to be related

 to discrete wavelengths and standing waves for certain orbits of the

 electron particle about the proton. (Rather than considering an actual

 standing wave structure for the electron itself.) From de Broglie's

 perspective, and from modern physics at that time, this solution had a

 certain charm. It maintained the particle - wave duality for BOTH light and

 matter, and at the same time explained why only certain orbits of the

 electron (which relate to whole numbers of standing waves) were allowed,

 which fitted beautifully with Niels Bohr model of the atom. de Broglie further

Fisika Kuantum                                                                    6
 explains his reasoning for the particle/wave duality of matter in his 1929

 Nobel Prize acceptance speech; On the one hand the quantum theory of

 light cannot be considered satisfactory since it defines the energy of a light

 particle (photon) by the equation E=hf containing the frequency f. Now a

 purely particle theory contains nothing that enables us to define a

 frequency; for this reason alone, therefore, we are compelled, in the case

 of light, to introduce the idea of a particle and that of frequency

 simultaneously. On the other hand, determination of the stable motion of

 electrons in the atom introduces integers, and up to this point the only

 phenomena involving integers in physics were those of interference and of

 normal modes of vibration. This fact suggested to me the idea that

 electrons too could not be considered simply as particles, but that

 frequency (wave properties) must be assigned to them also. (de Broglie,


 Quantum Theory: Erwin Schrodinger

 Schrodinger Wave Equations (1928)

 Quantum theory is essentially founded on the experimental observations of

 frequency     and     wavelength      for    both     light   and     matter.

 1. Planck's discovery that energy is related to frequency in the equation


 2. The Equivalence of Energy, Frequency and Mass E=hf=mc2, which

Fisika Kuantum                                                                    7
 deduces the Compton Wavelength Y=h/mc

 3. The de Broglie wavelength y=h/mv

 It was Erwin Schrodinger who discovered that when frequency f and de

 Broglie wavelength y were substituted into general wave equations it

 becomes possible to express energy E and momentum mv (from the above

 equations) as wave functions - thus a confined particle (e.g. an electron in

 an atom / molecule) with known energy and momentum functions could be

 described with a certain wave function. From this it was further found that

 only certain frequency wave functions, like frequencies on musical strings,

 were allowed to exist. These allowed functions and their frequencies

 depended on the confining structure (atom or molecule) that the electron

 was bound to (analogous to how strings are bound to a violin, and only

 then can they resonate at certain frequencies). Significantly, these allowed

 frequencies corresponded to the observed discrete frequencies of light

 emitted and absorbed by electrons bound in atoms/molecules. This further

 confirmed the standing wave properties of matter, and thus that only

 certain standing wave frequencies could exist which corresponded to

 certain energy states. The agreement of observed frequencies and

 Schrodinger's Wave Equations further established the fundamental

 importance of Quantum Theory and thus the Wave properties of both light

Fisika Kuantum                                                                  8
 and        matter.            As       Albert          Einstein      explains;

 How can one assign a discrete succession of energy values E to a system

 specified in the sense of classical mechanics (the energy function is a

 given function of the co-ordinates x and the corresponding momenta mv)?

 Planck's constant h relates the frequency f =E/h to the energy values E. It

 is therefore sufficient to assign to the system a succession of discrete

 frequency f values. This reminds us of the fact that in acoustics a series of

 discrete frequency values is coordinated to a linear partial differential

 equation (for given boundary conditions) namely the sinusoidal periodic

 solutions. In corresponding manner, Schrodinger set himself the task of

 coordinating a partial differential equation for a scalar wave function to the

 given energy function E (x, mv), where the position x and time t are

 independent variables. (Albert Einstein, 1936) It should also be noted that

 Schrodinger's wave equations describe scalar waves rather than vector

 electromagnetic      waves.    This   is   a    most    important   difference.

 Electromagnetic waves are vector waves - at each point in Space the wave

 equations yield a vector quantity which describes both a direction and an

 amplitude (size of force) of the wave, and this relates to the original

 construction of the e-m field by Faraday which described both a force and a

 direction of how this force acted on other matter particles. Scalar wave

 equations yield a single quantity for each point in space which simply

Fisika Kuantum                                                                     9
 describes the wave amplitude (there is no directional component). For

 example, sound waves are scalar waves where the wave amplitude

 describes the Motion (or compression) of the wave medium (air). With de

 Broglie's introduction of the concept of standing waves to explain the

 discrete energy states of atoms and molecules, and the introduction of

 scalar waves by Schrodinger, they had intuitively grasped important truths

 of nature as Albert Einstein confirms;

 Experiments on interference made with particle rays have given brilliant

 proof that the wave character of the phenomena of motion as assumed by

 the theory does, really, correspond to the facts.

 The de Broglie-Schrodinger method, which has in a certain sense the

 character of a field theory, does indeed deduce the existence of only

 discrete states, in surprising agreement with empirical facts. It does so on

 the basis of differential equations applying a kind of resonance argument.

 (Albert Einstein, 1927)

 Quantum Theory: Famous Quotes

 The more success the quantum theory has, the sillier it looks. (Albert

 Einstein to Heinrich Zangger, May 20, 1912)

 God    does    not   play   dice   with   the   cosmos.   (Albert   Einstein)

 I think that a 'particle' must have a separate reality independent of the

Fisika Kuantum                                                               10
 measurements. That is an electron has spin, location and so forth even

 when it is not being measured. I like to think that the moon is there even if I

 am not looking at it. (Albert Einstein)

 Einstein, don't tell God what to do. (Niels Bohr in response to Einstein)

 Those who are not shocked when they first come across quantum

 mechanics cannot possibly have understood it. (Niels Bohr on Physics)

 When it comes to atoms, language can be used only as in poetry. The

 poet, too, is not nearly so concerned with describing facts as with creating

 images. It is wrong to think that the task of physics is to find out how Nature

 is. Physics concerns what we say about Nature. (Niels Bohr, 1885-1962)

 Niels Bohr brainwashed a whole generation of physicists into believing that

 the problem (of the interpretation of quantum mechanics) had been solved

 fifty years ago. ( Murray Gell-Mann, Noble Prize acceptance speech, 1976)

 This statistical interpretation is now universally accepted as the best

 possible interpretation for quantum mechanics, even though many people

 are unhappy with it. People had got used to the determinism of the last

 century, where the present determines the future completely, and they now

 have to get used to a different situation in which the present only gives one

 information of a statistical nature about the future. A good many people find

 this unpleasant; Einstein has always objected to it. The way he expressed

 it was: "The good God does not play with dice". Schroedinger also did not

Fisika Kuantum                                                                 11
 like the statistical interpretation and tried for many years to find an

 interpretation involving determinism for his waves. But it was not successful

 as a general method. I must say that I also do not like indeterminism. I

 have to accept it because it is certainly the best that we can do with our

 present knowledge. One can always hope that there will be future

 developments which will lead to a drastically different theory from the

 present quantum mechanics and for which there may be a partial return of

 determinism. However, so long as one keeps to the present formalism, one

 has to have this indeterminism.

 (P.A.M. Dirac, "The Development Of Quantum Mechanics" Conferenza

 Tenuta il 14 Aprile 1972, in Roma, Accademia Nazionale dei Lincei, 1974)

 Both matter and radiation possess a remarkable duality of character, as

 they sometimes exhibit the properties of waves, at other times those of

 particles. Now it is obvious that a thing cannot be a form of wave motion

 and composed of particles at the same time - the two concepts are too

 different.                        (Heisenberg,                         1930)

 The solution of the difficulty is that the two mental pictures which

 experiment lead us to form - the one of the particles, the other of the waves

 - are both incomplete and have only the validity of analogies which are

Fisika Kuantum                                                               12
 accurate only in limiting cases. (Heisenberg, 1930)

 Light and matter are both single entities, and the apparent duality arises in

 the limitations of our language.

 It is not surprising that our language should be incapable of describing the

 processes occurring within the atoms, for, as has been remarked, it was

 invented to describe the experiences of daily life, and these consist only of

 processes involving exceedingly large numbers of atoms. Furthermore, it is

 very difficult to modify our language so that it will be able to describe these

 atomic processes, for words can only describe things of which we can form

 mental pictures, and this ability, too, is a result of daily experience.

 Fortunately, mathematics is not subject to this limitation, and it has been

 possible to invent a mathematical scheme - the quantum theory - which

 seems entirely adequate for the treatment of atomic processes; for

 visualisation, however, we must content ourselves with two incomplete

 analogies - the wave picture and the corpuscular picture. (Heisenberg,


 What we observe as material bodies and forces are nothing but shapes

 and variations in the structure of space. Particles are just schaumkommen

 (appearances).The world is given to me only once, not one existing and

 one perceived. Subject and object are only one. The barrier between them

 cannot be said to have broken down as a result of recent experience in the

Fisika Kuantum                                                                 13
 physical sciences, for this barrier does not exist. (Erwin Schrodinger) Let

 me say at the outset, that in this discourse, I am opposing not a few special

 statements of quantum mechanics held today (1950s), I am opposing as it

 were the whole of it, I am opposing its basic views that have been shaped

 25 years ago, when Max Born put forward his probability interpretation,

 which   was     accepted   by   almost   everybody.(Schrödinger      E,   The

 Interpretation of Quantum Mechanics. Ox Bow Press, Woodbridge, CN,

 1995).I don't like it, and I'm sorry I ever had anything to do with it. (Erwin

 Schrodinger talking about quantum mechanics) I think it is safe to say that

 no one understands quantum mechanics. (Richard Feynman on Physics)

 The next question was - what makes planets go around the sun? At the

 time of Kepler some people answered this problem by saying that there

 were angels behind them beating their wings and pushing the planets

 around an orbit. As you will see, the answer is not very far from the truth.

 The only difference is that the angels sit in a different direction and their

 wings push inward. (Richard Feynman, Character Of Physical Law) One

 does not, by knowing all the physical laws as we know them today,

 immediately obtain an understanding of anything much. (Richard Feynman,

 1918-1988)    I love only nature, and I hate mathematicians. (Richard

 Feynman 1918-1988) ... the more you see how strangely Nature behaves,

 the harder it is to make a model that explains how even the simplest

Fisika Kuantum                                                                14
 phenomena actually work. So theoretical physics has given up on that.

 (Richard                       Feynman                          1918-1988)

 What I am going to tell you about is what we teach our physics students in

 the third or fourth year of graduate school... It is my task to convince you

 not to turn away because you don't understand it. You see my physics

 students don't understand it. ... That is because I don't understand it.

 Nobody does. (Feynman, Richard P. Nobel Lecture, 1966, 1918-1988,

 QED, The Strange Theory of Light and Matter)

Fisika Kuantum                                                              15

To top