consider Three-Dimensional harmonic oscillator with the same frequencies along all three directions. a) determine the wave...

consider Three-Dimensional harmonic oscillator with the same frequencies along all three directions. a) determine the wave function and the energy of the ground state. b) how many quantum numbers are needed to describe the state of oscillation? c) the degeneracy of the first excited state. express the wave function involved in the schrodinger equation as a product given by x, y, z and separate the variables.

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genius_generous answered 1 year ago

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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Consider a particle of mass m moving in a two-dimensional harmonic oscillator potential : U(x,y)=...

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QUANTUM MECHANICS-upper level In the harmonic oscillator problem, the normalized wave functions for the ground and first excited states are ψ0 and ψ1. Using these functions, at some point t, a wave function u = Aψ0 + Bψ1 is constructed, where A and B are real numbers. (a) Show that the average value of x in the u state is generally non-zero. (b) What condition A and B must satisfy if we want the function u to be normalized? (c)...

Construct the explicit form of the lowest three eigenfunctions of the harmonic oscillator.

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