Question

Consider an infinitely deep potential well of width 2a centered at x = 0.

The probability of finding a particle of mass m in the ground, first and

second excited state is 60%, 30% and 10% respectively. What is the energy

expectation value of the particle ?

Answer 1

Permitted energy level for n^th state, $E=\dfrac{n^{2}h^{2}}{8ml^2}$

For Ground state, n=1

$E_1=\dfrac{1^2\times(4.135\times10^{-15})^2}{8\times9.1\times10^{-31}\times4a^2}\\ E_1=\dfrac{0.587}{a^2}eV$

For First Excited state, n=2

$E_2=\dfrac{(2)^2\times0.587}{a^2}=\dfrac{2.34}{a^2}eV$

For Second Excited state, n=3

$E_3=\dfrac{9\times0.587}{a^2}=\dfrac{5.283}{a^2}eV$