Quantum Mechanics; Expectation value

[Stephen_G]

Homework Statement

At t=0, the system is in the state

. What is the expectation value of the energy at t=0?

I'm not sure if this is straight forward scalar multiplication, surprised if it was, but we didn't cover this in class really, just glossed through it. If someone could walk me through this, it would be most appreciated.

Homework Equations

The Attempt at a Solution

I just multiplied the 1/sqrt2 by 1 and i. I'm certain that this is not the correct.

 

[mfb]

I just multiplied the 1/sqrt2 by 1 and i.

How, and why?

You need to know the energies of the two states, at least as variables.

If you measure which state the particle is in, what are the possible results? What is the energy associated with each result? What is the probability?

 

[Stephen_G]

Would the energies be the eigenvalues? I got those in the first portion of that question.

The first question asked for the eigenvlaues and vectors for the hamiltonian:

 

[mfb]

Please post the full question with all relevant context, otherwise there is too much guesswork involved.

In general, how do you find the expectation value of an operator?

 

[Stephen_G]

Sorry about that, I will in the future.
But, for the your question, you would just insert your expectation value into your braket <Ψ|A|Ψ> and solve, correct?

 

[mfb]

That works, sure.