Quantum mechanics as a classical theory

1985 ◽  
Vol 31 (6) ◽  
pp. 1341-1348 ◽  
Author(s):  
André Heslot
Keyword(s):  
Quantum Mechanics ◽  
Classical Theory

scholarly journals Relativistic quantum mechanics

1932 ◽  
Vol 136 (829) ◽  
pp. 453-464 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Classical Theory ◽  
Correspondence Principle ◽  
Relativistic Quantum ◽  
Classical Mechanics ◽  
Hamiltonian Function ◽  
Relativistic Quantum Mechanics ◽  
Classical Electrodynamics ◽  
Quantum Phenomena

The steady development of the quantum theory that has taken place during the present century was made possible only by continual reference to the Correspondence Principle of Bohr, according to which, classical theory can give valuable information about quantum phenomena in spite of the essential differences in the fundamental ideas of the two theories. A masterful advance was made by Heisenberg in 1925, who showed how equations of classical physics could be taken over in a formal way and made to apply to quantities of importance in quantum theory, thereby establishing the Correspondence Principle on a quantitative basis and laying the foundations of the new Quantum Mechanics. Heisenberg’s scheme was found to fit wonderfully well with the Hamiltonian theory of classical mechanics and enabled one to apply to quantum theory all the information that classical theory supplies, in so far as this information is consistent with the Hamiltonian form. Thus one was able to build up a satisfactory quantum mechanics for dealing with any dynamical system composed of interacting particles, provided the interaction could be expressed by means of an energy term to be added to the Hamiltonian function. This does not exhaust the sphere of usefulness of the classical theory. Classical electrodynamics, in its accurate (restricted) relativistic form, teaches us that the idea of an interaction energy between particles is only an approxi­mation and should be replaced by the idea of each particle emitting waves which travel outward with a finite velocity and influence the other particles in passing over them. We must find a way of taking over this new information into the quantum theory and must set up a relativistic quantum mechanics, before we can dispense with the Correspondence Principle.

From Classical to Quantum Mechanics

2021 ◽  
pp. 207-219
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Harmonic Oscillator ◽  
Path Integral ◽  
Classical Theory ◽  
Constrained Systems ◽  
Experimental Results ◽  
Basic Assumptions ◽  
Original Approach

In Chapter 2 we presented the method of canonical quantisation which yields a quantum theory if we know the corresponding classical theory. In this chapter we argue that this method is not unique and, furthermore, it has several drawbacks. In particular, its application to constrained systems is often problematic. We present Feynman’s path integral quantisation method and derive from it Schroödinger’s equation. We follow Feynman’s original approach and we present, in addition, more recent experimental results which support the basic assumptions. We establish the equivalence between canonical and path integral quantisation of the harmonic oscillator.

scholarly journals Models on the boundary between classical and quantum mechanics

2015 ◽  
Vol 373 (2047) ◽  
pp. 20140236 ◽  
Author(s):  
Gerard 't Hooft
Keyword(s):  
Quantum Mechanics ◽  
Classical Theory ◽  
Classical Logic ◽  
Quantum Systems ◽  
Bell's Theorem ◽  
Vacuum Fluctuations ◽  
Superstring Theory ◽  
Quantum Models ◽  
Physical Laws ◽  
Classical And Quantum Mechanics

Arguments that quantum mechanics cannot be explained in terms of any classical theory using only classical logic seem to be based on sound mathematical considerations: there cannot be physical laws that require ‘conspiracy’. It may therefore be surprising that there are several explicit quantum systems where these considerations apparently do not apply. In this report, several such counterexamples are shown. These are quantum models that do have a classical origin. The most curious of these models is superstring theory. So now the question is asked: how can such a model feature ‘conspiracy’, and how bad is that? Is there conspiracy in the vacuum fluctuations? Arguments concerning Bell's theorem are further sharpened.

scholarly journals The scattering of α-particles in helium

1930 ◽  
Vol 128 (807) ◽  
pp. 114-122 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Classical Theory ◽  
Classical Mechanics ◽  
Wave Mechanics ◽  
Α Particles

The problem of the collision of two particles which act upon each other with forces varying as the inverse square of the distance between them has been solved exactly on the basis of the new quantum mechanics, and the solution is the same as that given by classical mechanics. In a recent paper, however, Mott has pointed out that this agreement between the predictions of classical mechanics and wave mechanics depends upon the dissimilarity of the colliding particles; if the particles are identical the scattering laws given by the wave mechanics will be very different from those of classical theory. Mott has considered the two types of collision between similar particles, (1) in which the particles possess spin, such as the collisions of electrons with electrons or protons with hydrogen nuclei, and (2) in which the particles have no spin, such as the collisions of α -particles with helium nuclei.

scholarly journals Relativity quantum mechanics with an application to compton scattering

1926 ◽  
Vol 111 (758) ◽  
pp. 405-423 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Poisson Bracket ◽  
Classical Theory ◽  
Analytic Functions ◽  
Algebraic Theory ◽  
Dynamical Theory ◽  
Canonical Variables ◽  
Algebraic Laws ◽  
Points Of View

The new quantum mechanics, introduced by Heisenberg and since developed from different points of view by various authors, takes its simplest form if one assumes merely that the dynamical variables are numbers of a special type (called q-numbers to distinguish them from ordinary or c-numbers) that obey all the ordinary algebraic laws except the commutative law of multiplication, and satisfy instead of this the relations q r q s – q s q r =0, p r p s – p s p r = 0 } q r q s – p s q r = 0 ( r ≠ s ) or ih ( r = s ) where the p' s and q' s are a set of canonical variables and h is a c-number euqal to (2π) -1 times the usual Planck’s constant. Equations (1) may be regarded as replacing the commutative law of the classical theory, as one can, with their help, build up a complete algebraic theory of quantities that are analytic functions of a set of canonical variables. Further, it may easily be seen that the quantity [ x, y ] defined by xy – yz = ih [ x, y ] is completely analogous to the Poisson bracket of the classical theory. By means of this analogy the whole of the classical dynamical theory, in so far as it can be expressed in terms of P. B.’s instead of differential coefficients, may be taken over immediately into the quantum theory.

Quantum Theory

2018 ◽  
Author(s):  
Kate Atkinson
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Quantum System ◽  
20Th Century ◽  
Classical Theory ◽  
Theoretical Physics ◽  
Early 20Th Century ◽  
Max Planck ◽  
Physical Phenomena

Developed in the early 20th century, quantum theory is a branch of theoretical physics that concerns the unpredictable quality of particles at the quantum, or subatomic, level. In 1900 Max Planck (1859–1947) inaugurated inquiry into quantum mechanics when he challenged the classical theory that light behaves as a wave, proposing instead that it is emitted in quanta, or discrete units. By 1927 this groundbreaking theory had been more clearly articulated by Niels Bohr’s (1885–1962) "Principle of Complementarity" and Werner Heisenberg’s (1901–1976) "Uncertainty Principle." Heisenberg proposed that all physical phenomena that can be observed are subject to a degree of indeterminacy and suggested that the act of scientific observation of a quantum system would change that system. These new proposals of quantum theory unseated the authority of classical deterministic physics and challenged the perceived objectivity of science. Attracted by quantum theory’s revolutionary ideas, various modernist critics adapted its principles of uncertainty and indeterminacy to studies in the humanities. For instance, I. A. Richards (1893–1970) and William Empson (1906–1984) employed Bohr’s concepts in their work on irony, ambiguity, and paradox. Heisenberg suggested, however, that both modern artistic innovations and quantum theory were the products of "profound transformations in the fundamentals of our existence" (1958: 95).

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