(adsbygoogle = window.adsbygoogle || []).push({}); 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

u_{1}(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])u_{1}(q)=Eu_{1}(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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# Hamiltonian of the Quantum Harmonic Oscillator-Eigenfunction & Eigenvalue

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