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Calcifur
#1
Feb5-12, 11:30 AM
P: 18
1. The problem statement, all variables and given/known data
Show that the equation below is an eigenfunction for the Quantum Harmonic Oscillator Hamiltonian and find its corresponding eigenvalue.


2. Relevant equations
u1(q)=A*q*exp((-q[itex]^{2}[/itex])/2)


3. The attempt at a solution
Ok, so I know that the Quantum Harmonic Oscillator Hamiltonian (H[itex]_{QHO}[/itex]) is :
(H[itex]_{QHO}[/itex])=[itex]\frac{1}{2}[/itex][itex]\hbar[/itex]ω(((-d^2)/(dq^2))+q^2) and I know that:
(H[itex]_{QHO}[/itex])u1(q)=Eu1(q)

but how do I show that it's an eigenfunction? Simply subbing it into the eqn doesn't appear to help.

Many thanks in advance.
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