Particle moving in a one-dimensional potential

AI Thread Summary
The discussion centers on the wavefunction of a particle in a one-dimensional potential, specifically Psi(x,0) = A(x-a)x for 0 <= x <= a and 0 otherwise. Participants clarify that the wavefunction does not need to be periodic, as it serves as a probability amplitude rather than a traditional wave. The confusion arises from the expectation that wavefunctions should resemble periodic functions, which is not a requirement. The conversation also touches on the mathematical representation of wave motion, emphasizing that a wave can be non-periodic, like a pulse. Understanding the nature of wavefunctions is crucial for solving the problem accurately.
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Homework Statement



A particle moving in a one-dimensional potential is in a state such that its wavefunction at time t=0 is:

Psi(x,0)=A(x-a)x, 0<=x<=a, and
Psi(x,0)=0, otherwise.

Sketch |Psi(x,0)|^2, which gives the probability distribution describing the position of the particle at time t=0.

Homework Equations



As above

The Attempt at a Solution



I am thrown by Psi in this question. It doesn't even resemble a wavefunction. Am I simply supposed to square the absolute value of the polynomial?
 
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Yes. Why do you say it "doesn't even resemble a wavefunction"?
 
Because its not a periodic function.
 
I'm obviously overlooking something important here. Please help.
 
Why should it be periodic? Are sure what is meant by a "waveform" here?
 
Shouldn't a wavefunction resemble a wave? ie be periodic?
 
You are confusing a wavefunction with a periodic function such as a sinusoid of varying harmoics, etc. The wavefunction is essentially a probability amplitude for (in this case) the location of a particle.

It is, (in this case) a one dimensional wave and you can model its motion using a (rather famous) relation that looks quite close to the wave equation, shown here:

[ tex ] \nabla^2 f(x,y,z) = \frac{1}{c^2} \frac{\partial f(x,y,z)}{\partial t} [ /tex ]
 
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Identify said:
Shouldn't a wavefunction resemble a wave? ie be periodic?
Nope. A pulse traveling down a string, for instance, is a wave. There's no requirement for periodicity at all.
 
by the way...why isn't my tex being formatted?
 
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