I have not found a way to develop Schrodinger Ensemble Theory for the time-dependent Schrodinger Equation. The expectation energy averaged across the entire ensemble remains the eigenvalue E, but the energy of any individual particle is always computed fromĪlso note that since psi(x) and phi(p) only represent initial conditions placed on the ensemble, the subsequent development of the ensemble over time is determined by applying Liouville's theorem to the ensemble. Please note that for these Schrodinger ensembles, total particle energy is not a "sharp" variable. Even then, there will still be some freedom left to decide on the direction of the momentum vectors. Otherwise, it might be possible to integrate each side of the relationship separately and isolate p(x) from the result.
#Schrodinger theory trial#
On the one hand, it may be possible to find p(x) by inspection or via trial and error. \( \psi(x)\psi(x)*dx = \phi(p)\phi(p)*dp \) is satisfied.įinally, I use this consistency relationship to seek a momentum function p(x). That is, I require that my consistency relationship That is, I insist that the fraction of ensemble particles initially positioned in the region (x, x + dx) equals the fraction of ensemble particles with initial values of momentum in the region (p, p + dp). I then require that the fractional density functions be consistent across the two spaces - real space and momentum space. \( \psi(x) \) are Fourier transforms of each other according to the usual rules. Devised in 1935 by the Austrian physicist Erwin Schrödinger, this thought experiment was designed to shine a spotlight on the difficulty with interpreting quantum theory. Suppose, in addition, that these particles exhibit an initial momentum distribution such that the fraction of particles with momentum in the range (p, p + dp) is given by \( \phi\phi*dp \), where \( \phi(p) \) and A cat is locked up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter. Schrödinger wrote: One can even set up quite ridiculous cases. Erwin Schrödinger suggested it in 1935, in reaction to the Copenhagen interpretation of quantum physics. Suppose further that an ensemble of identical, non-interacting particles is distributed in real space at time t=0 such that the fraction of particles in the region (x, x + dx) is given b y Schrödingers cat is a thought experiment about quantum physics.
Is the solution to the Schrodinger equation in the form : For a given potential V(x), suppose \(\psi(x)\) The work will generalize when I deal with the hydrogen atom. The first group of examples I will discuss are all one-dimensional. a particle in an infinite potential well,.Some years ago, I chose to pursue a different approach to the study of the time-independent Schrodinger equation, particularly as it is commonly applied to the following situations: Introduction to Schrodinger Ensemble Theory