# QM Problems with wavefunction given in sin and cos.

1. Mar 12, 2006

### darkar

Well, the question goes like this,

A particle of mass m is trapped in an infinitely deep one-dimensional potential well between x = 0 and x = a and at a time t=0,, the wave fuction is given as

Φ(x,t=0)=sin(((πx)/a))cos(((2πx)/a))

(i) What possible values may be found for energy of particle?
(ii) What is the expected (or average) value of the energy of the particle?

Well, we got the hints of using
sinAcosA = (1/2){sin(A+B)+sin(A-B)}

We got (1/2){sin(3*pi*x/a) - sin(pi*x/a)}.... but not sure what to do next.

2. Mar 12, 2006

### Physics Monkey

Those sure look like energy eigenstates to me.

3. Mar 12, 2006

### topsquark

What is the definition of an expectation value? (Hint: It's involves an integral over the state of the system.)

-Dan

4. Mar 12, 2006

### darkar

The definition of expected value shd be integration of f(x) * psi^2 dx. Am i rite?

Well, the biggest problem is how shd we start, what can u say abt a wave function with (1/2){sin(A+B)+sin(A-B)}?

5. Mar 13, 2006

### cepheid

Staff Emeritus
And in DIRECT response to the above comment:

Does that make it a bit more obvious? I didn't bother checking to see if you did your trig right, but if you did, then you have a linear combination of eigenfunctions for the infinite square well problem. That should make it pretty clear how to proceed.

6. Mar 13, 2006

### darkar

Umm, well, theres another thing, if u do integration of square of the given psi^2, u get a/4 instead of 1, shouldnt it be 1?

7. Mar 13, 2006

### darkar

Umm, all rite, got it , i need to normalize the equation.

Thanks for the hints everyone ~