What Are the Quantum Mechanics of a Particle in a 1-D Box?

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In summary, the conversation discusses a particle moving in a 1-D box with a potential that is zero in the region and infinite at the walls and elsewhere. It covers the possible results and relative probabilities of measuring the energy of the system, the possible forms of the wave function after the measurement, and the relative probabilities of the possible outcomes if the energy is immediately re-measured. The individual asking for help has the wavefunction at a particular time and the energy eigenvalues and eigenfunction, but is struggling with figuring out the next steps. They mention attempting to find the overlap integral of the wavefunction and eigenfunction, but are having difficulties. Another individual asks for help as well, stating they are also having trouble getting started and would appreciate any
  • #1
swain1
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A particle moving in a 1-D box subject to a potential that is zero in the region and infinite at the walls and elsewhere.

(a) Determine the possible results of the measurement of the energy of this system and their relative probabilities. (b) What are the possible forms of the wave function immediately after such a measurement? (c) If the energy is immediately re-measured, what now will be the relative probabilities of the possible outcomes?

For this question I have the wavefunction at a paticular time and also the energy eigenvalues and eigenfunction. I understand the maths involved but I am struggling with working out what I have to do. I would be grateful of any help. Thanks
 
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  • #2
well if you have the energy eigenvalues, you are done with part a, if you have the wavefunction you are done with part b, so it seems like you are well on your way. Part c wants you to realize that in quantum mechanics, a measurement collapses the wave function, google "quantum mechanics wavefunction collapse".
 
  • #3
swain1 said:
A particle moving in a 1-D box subject to a potential that is zero in the region and infinite at the walls and elsewhere.

(a) Determine the possible results of the measurement of the energy of this system and their relative probabilities. (b) What are the possible forms of the wave function immediately after such a measurement? (c) If the energy is immediately re-measured, what now will be the relative probabilities of the possible outcomes?

For this question I have the wavefunction at a paticular time and also the energy eigenvalues and eigenfunction. I understand the maths involved but I am struggling with working out what I have to do. I would be grateful of any help. Thanks
So what did you get so far ? Formula's please...Starting from those, we can help you on your way.

Regards
marlon
 
  • #4
Thats really the problem I have is getting started. What I have tried is to work out the overlap integral of my wavefunction and the eigenfunction but I just have a horrible integration that I can't do and I don't know if I am going about it in the right way?
 
  • #5
im trying to do that same exercise, but i don't know how to start, I am really having trouble with this one, could anyone give me a hand?
 

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