Schrödinger Gas Model

In addition to long time collaborators Leopold Infeld, Nathan Rosen, Peter Bergmann and others, Einstein also had some one-shot collaboratio...

Phys Rev Lett. 2001 Feb 19;86(8):1402-5.

Unpublished letters of late 1925 between Einstein and Schrödinger and the doctoral thesis of de Broglie reveal sources of Schrödinger’s inspiration to invent wave mechanics. Schrödinger saw a congenial similarity of de Broglie’s work on the stability of the atom with his own earlier speculation in relativity, which he noted to Einstein. But the last chapter of de Broglie’s thesis, on quantum statistics of gases, which is unfamiliar to many modern readers, provided Schrödinger with the method of treatment of a gas of material particles considered as a system of modes of vibration, of ’’matter waves.’’ This method especially, and other successes of de Broglie’s ’’ingenious thesis,’’ convinced Schrödinger to take seriously the first part, on the conditions of stability of the atom in a wave picture. Thus he sought and found an equation to describe the states of the electron from the matter‐wave viewpoint.

Einstein suggested to Erwin Schrodinger that he might be able to reproduce the statistics of a Bose–Einstein gas by considering a box. Then to each possible quantum motion of a particle in a box associate an independent harmonic oscillator. Quantizing these oscillators, each level will have an integer occupation number, which will be the number of…

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A general class of discrete unitary models are described whose behavior in the continuum limit corresponds to a many-body Schrodinger equation. On a quantum computer, these models could be used to simulate quantum many-body systems with an exponential speedup over analogous simulations on classical computers.

In solid-state physics, the free electron model is a simple model for the behaviour of valence electrons in a crystal structure of a metallic solid.

Einstein suggested to Erwin Schrödinger that he might be able to reproduce the statistics of a Bose–Einstein gas by considering a box. The...

BRUCE M. BOGHOSIAN Center for Computational Science Boston University

Bruce M. Boghosian and Washington Taylor Iv, Int. J. Mod. Phys. C 08, 705 (1997). https://doi.org/10.1142/S0129183197000606