# Homework Help: Wavepackets, expressed as eigenstates. Calculate time to tunnel to adjacent pot well?

1. Jan 19, 2010

### squaric

1. The problem statement, all variables and given/known data

http://img29.imageshack.us/img29/5236/phst.jpg [Broken]

2. Relevant equations

http://img25.imageshack.us/img25/8815/11203939.jpg [Broken]

I need to find the equation for the question.

3. The attempt at a solution

a)

A bunch of waves/wave functions, that have phases/amplitudes that interfere constructively.

b)

|Y(x,t)|Squared = Co(/)0 + C1(/)1 Squared ???

c)

No idea

d)
i)

A graph that slopes down, (qe) to then up to a peak, (Difference between each point is Ea) then finally back down to q.
ii)

Down then up then to a straight like across.

I'd also like to know how to work out the time taken to travel to an adjacent potential well assuming Y(x,t=0) = Co(/)0 + C1(/)1
I think (/)0 and (/)1 are the lowest eigenstates and C0 and C1 are just coefficients.

(I think the original thread was posted in the wrong section!)

Last edited by a moderator: May 4, 2017
2. Jan 23, 2010

### Maxim Zh

Re: Wavepackets, expressed as eigenstates. Calculate time to tunnel to adjacent pot w

The complete solution was deleted (it's not allowed). So if you didn't see it:

(a) ------------------------------

The waves must interfer constructively only over a region.

(b) ------------------------------

You have forgotten some time-dependent terms.

(c) ------------------------------

The correct solution of (b) contains a periodic time function. It's period is the answer