Calculate E Min: n=1, L=2a, ψ=2 - Help!

[tanaygupta2000]

Homework Statement

A particle is confined in a one dimensional potential box with impenetrable walls at x = ±a. Its energy eigenvalue is 2eV and corresponds to the eigenfunction of the first excited state. What is the lowest possible energy of the particle ?

Relevant Equations

Hψ = Eψ
E = (nπ hbar)^2/2mL^2

For calculating minimum E, I have n = 1, L = 2a & ψ = 2.
But I am not getting how to exactly find its value.
Please help me !

 

[PeroK]

Homework Statement:: A particle is confined in a one dimensional potential box with impenetrable walls at x = ±a. Its energy eigenvalue is 2eV and corresponds to the eigenfunction of the first excited state. What is the lowest possible energy of the particle ?
Relevant Equations:: Hψ = Eψ
E = (nπ hbar)^2/2mL^2

For calculating minimum E, I have n = 1, L = 2a & ψ = 2.
But I am not getting how to exactly find its value.
Please help me !

What is $\psi = 2$ supposed to mean?

 

[kuruman]

Its energy eigenvalue is 2eV and corresponds to the eigenfunction of the first excited state.

What does this statement imply about the value of the quantity $\dfrac{\pi^2\hbar^2}{2ma^2}$?

 

[tanaygupta2000]

What does this statement imply about the value of the quantity $\dfrac{\pi^2\hbar^2}{2ma^2}$?

The value of this quantity should be equal to 2 × 1.6e-19 J

 

[PeroK]

The value of this quantity should be equal to 2 × 1.6e-19 J

Why is that?

 

[tanaygupta2000]

Why is that?

Since this is quantized energy and it is given that the value of energy eigenvalue is 2eV

 

[PeroK]

Since this is quantized energy and it is given that the value of energy eigenvalue is 2eV

Which eigenvalue is $2eV$? $n = 1$ or $n = 2$?

 

[tanaygupta2000]

Which eigenvalue is $2eV$? $n = 1$ or $n = 2$?

First excited state, n=1

 

[kuruman]

First excited state, n=1

So the ground state is n = 0?

 

[PeroK]

First excited state, n=1

And which energy eigenstate are you trying to find?

 

[tanaygupta2000]

Okay now I think I got it. The given value is for n=2 and I need to find it for n=1. Right ?

 

[PeroK]

Okay now I think I got it. The given value is for n=2 and I need to find it for n=1. Right ?

Right!