Calculating Transition Probability for Particle Mass "m

In summary, after the potential well expands, the wave function of the system is still the ground state wave function for the narrow well. Calculate the transition probability for the particle to go from the ground state to the first excited state.
  • #1
amarante
44
6
I need some help how can I calculate a transition probability on this problem: A particle of mass "m" on a potential well (1), where it V(x) is infinite for x>L/2 and for x<L/2 . Inside the region V(x)=0 . I know how I get the eigenfunctions and the Energy.
But, than the potential (2) well expands instantly and now it is infinite for x>L and x<L . and it is zero inside that region.

I have to calculate the probability that the particle on the ground state for the potential 1 will go to the first excited state on the potential 2.

Should I use pertubation theory and consider this expansion of the potential as a pertubation? And if yes, how do I write this pertubation?

Thanks in advance
 
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  • #2
amarante said:
I need some help how can I calculate a transition probability on this problem: A particle of mass "m" on a potential well (1), where it V(x) is infinite for x>L/2 and for x<L/2 . Inside the region V(x)=0 . I know how I get the eigenfunctions and the Energy.
But, than the potential (2) well expands instantly and now it is infinite for x>L and x<L . and it is zero inside that region.

I have to calculate the probability that the particle on the ground state for the potential 1 will go to the first excited state on the potential 2.

Should I use pertubation theory and consider this expansion of the potential as a pertubation? And if yes, how do I write this pertubation?

Thanks in advance

I think that you're making the question harder than it actually is.

Immediately after the expansion, the wave function of the system is still the ground state wave function for the narrow well. What is the wave function for the first excited state of system immediately after the expansion?

Use these two wave functions to calculate the transition probability.
 
  • #3
I recall a very similar problem from Griffiths' QM. You might want to take a look.
 

What is the formula for calculating transition probability for particle mass "m"?

The formula for calculating transition probability for particle mass "m" is P = |(x)|^2, where (x) is the wavefunction of the particle.

How is the transition probability related to the particle mass "m"?

The transition probability is directly proportional to the particle mass "m". This means that as the particle mass increases, the transition probability also increases.

Can the transition probability be calculated for any particle mass "m"?

Yes, the transition probability can be calculated for any particle mass "m" as long as the wavefunction (x) is known.

What is the significance of calculating transition probability for particle mass "m"?

Calculating transition probability for particle mass "m" allows us to understand the behavior and movement of particles in quantum mechanics. It helps us determine the likelihood of a particle transitioning from one state to another.

Are there any limitations to using transition probability to calculate particle mass "m"?

Yes, there are limitations to using transition probability to calculate particle mass "m". This method is only applicable in quantum mechanics and cannot be used for particles in classical mechanics. Additionally, it assumes that the particle is in a well-defined energy state and does not take into account any external factors that may affect the particle's movement.

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