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17 Nov 2019
The Schrodinger equation for a one-dimensional harmonic oscillator may be written -h^2/2 mu d^2 psi/dx^2 + 1/2 kx^2 psi = E psi where mu is the effective mass of the oscillator and times is the displacement from the equilibrium position. Show that the wave function psi = Ae^ax^2, where A is a constant and alpha = (k mu)^1/2/2h, satisfies the Schrodinger equation. Hint, use a throughout the derivation, but at some point you will need to substitute alpha = (k mu)^1/2/2h back into the equation to make things simplify. What is the Energy, E? Note that E is a constant and CANNOT DEPEND ON x.
The Schrodinger equation for a one-dimensional harmonic oscillator may be written -h^2/2 mu d^2 psi/dx^2 + 1/2 kx^2 psi = E psi where mu is the effective mass of the oscillator and times is the displacement from the equilibrium position. Show that the wave function psi = Ae^ax^2, where A is a constant and alpha = (k mu)^1/2/2h, satisfies the Schrodinger equation. Hint, use a throughout the derivation, but at some point you will need to substitute alpha = (k mu)^1/2/2h back into the equation to make things simplify. What is the Energy, E? Note that E is a constant and CANNOT DEPEND ON x.
Elin HesselLv2
19 Sep 2019