Solving the Wave Function: Find Ea, q, and Time?

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SUMMARY

The discussion focuses on solving a wave function problem involving the calculation of energy (Ea), charge (q), and time in quantum mechanics. The user attempts to derive the equation for the wave function, indicating that the solution requires understanding of wave interference and periodic functions. Key insights include the necessity of incorporating time-dependent terms into the wave function and recognizing the significance of eigenstates and coefficients in the solution. The correct approach involves identifying the periodic nature of the wave function to determine the time taken to travel between potential wells.

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  • Quantum mechanics fundamentals
  • Wave function analysis
  • Understanding of eigenstates and coefficients
  • Knowledge of periodic functions in physics
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  • Explore time-dependent Schrödinger equations
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Students and professionals in physics, particularly those focusing on quantum mechanics, wave functions, and energy calculations in potential wells.

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Homework Statement



http://img29.imageshack.us/img29/5236/phst.jpg

Homework Equations



http://img25.imageshack.us/img25/8815/11203939.jpg

I need to find the equation for the question.

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:
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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
 

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