# Particle in a 1D box

## Homework Statement

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

## 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

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TSny
Homework Helper
Gold Member
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?

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 Schrodinger's ψ^2

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

TSny
Homework Helper
Gold Member
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.

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

TSny
Homework Helper
Gold Member
Amazing! Good luck with your studies and welcome to Physics Forums.