Particle in 1D Box: Relationship to Probability & Energy

[Ayham]

Homework Statement

I have a question: what's the relationship between the probability of finding the particle and the particle's energy? if x is the same.

Homework Equations

The Attempt at a Solution

the first question i had 30% for ground state
2nd energy level i got 2%
3rd energy level i got 16%
is that right? they're between 2L/3 and L/2

 

[TSny]

Your answers for the n = 1 and n = 3 states look correct. But not for the n = 2 state.

If you show your work, we can see if your method is correct.

I'm not sure I fully understand the question. Are you suppose to derive a functional relationship, P(n), between the probability P of finding the particle between L/2 and 2L/3 and the quantum number n?

 

[Ayham]

i'll check my 2nd right away, my question is "if the energy state increases does the probability decreases?"
the equation for the answer is done by Schrödinger's ψ^2

 

[Ayham]

I found my mistake... looks like the 2nd is 9.7% does that make sense? can u answer my previous question please?

 

[TSny]

Your answers now look pretty good (I got 9.8% for n = 2 and 17% for n = 3).

If you look at your three results, you can see that the probability decreases in going from n = 1 to n = 2 and then increases when going from n = 2 to n = 3. So, the probability does not increase or decrease monotonically as n increases. However, the probabilities will all tend to approach a common value (the classical result) as n increases to large values.

 

[Ayham]

ok Thanks :) I am just 14 and i started quantum a few days ago, plus I am new here

 

[TSny]

Amazing! Good luck with your studies and welcome to Physics Forums.