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