Hey! Sign in to get help with your study questionsNew here? Join for free to post

Showing two 1D box potentials merge into a 2D

Announcements Posted on
Four hours left to win £100 of Amazon vouchers!! Don't miss out! Take our short survey to enter 24-10-2016
    • Thread Starter

    Click here for question

    So I showed

    U_1(x) = \begin{Bmatrix} 0, \ 0<x<a \\ 0, \ ow

    is represented by the eigenfunction

    \phi_n(x) = \sqrt{\dfrac{2}{a}} sin \dfrac{n \pi x}{a}, \ n=1,2,3...

    with eigenenergies

    E_n = \dfrac{\hbar^2 n^2 \pi ^2}{2ma^2}

    Then to show that the 2D box

    U_2(x) = \begin{Bmatrix} 0, \ 0<x<a, \ 0<y<a \\ 0, \ ow

    is represented by the eigenfunction

    \psi_{{n_x},{n_y}}(x,y) = \phi_{n_x}(x) \phi_{n_y}(y) = \dfrac{2}{a}sin \dfrac{n_x \pi x}{a} sin \dfrac{n_y \pi y}{a}

    with eigenenergies

    E_{{n_x},{n_y}} = E_{n_x}+E_{n_y} = \dfrac{\hbar^2 \pi^2}{2ma^2}(n_x^2 + n_y^2)

    Is it sufficient to simply state that by separating the variables, and letting \psi_{{n_x},{n_y}} = f(x)g(y), one can separate the 2D box into two independent 1D boxes?

    Just to clarify here, I'm not explicitly asked to separate the 2D box, but to show that two 1D boxes will combine into a 2D box... so is it okay to just say that, "since we can seperate the 2D box eigenfunction into two 1D box eigenfunctions, it is clear that the 2D eigenfunction is a combination of two 1D eigenfunctions."

    Yeah, just assume you can always separate variables.
Write a reply…


Submit reply


Thanks for posting! You just need to create an account in order to submit the post
  1. this can't be left blank
    that username has been taken, please choose another Forgotten your password?
  2. this can't be left blank
    this email is already registered. Forgotten your password?
  3. this can't be left blank

    6 characters or longer with both numbers and letters is safer

  4. this can't be left empty
    your full birthday is required
  1. Oops, you need to agree to our Ts&Cs to register
  2. Slide to join now Processing…

Updated: May 11, 2012
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

What do you wear to bed?
Useful resources

Make your revision easier


Maths Forum posting guidelines

Not sure where to post? Read here first


How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups
Study resources

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.