What is the Lowest Energy State of a Simple Harmonic Oscillator?

[fredrick08]

Homework Statement

The wave function \Psi(x,t) ofr the lowest energy state of simple harmonic oscillator, consisting of a particle mass m acted on by a linear restoring force F=Cx, where C is the force constant, can be expressed as..
\Psi(x,t)=Aexp[-(\sqrt{}Cm/2h)x^{}2-(i/2)(\sqrt{}C/m)t] where A is constant.

a. use the Hamiltonian operator with V(x)=.5x^{}2, to evaluate the total energy of the state!

Homework Equations

Hop(x)=(P^{}2op/2m)+V(x)
Hop(t)=i*hbar(d/dt)
P^{}2op=-hbar^{}2d^{}2/dx^{}2

The Attempt at a Solution

ok i am very confused as to which operqator to use, since my wave function is not time independent, but they give me V(x) value...
but to find to total energy all u do is multiply the operator by wave function i think.

can i ask which op do i use?? and is it just multiplying them together?

 

[latentcorpse]

they should give the same answer as its the same state!

but seeing as it says in the question to use the Hamiltonian with V(x)=\frac{1}{2}x^2, i'd use the first one you wrote down seeing as it has a V(x) term in it.

 

[fredrick08]

ok thanks