1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: One-dimensional infinitely high walls pit

  1. Jun 23, 2012 #1
    Hello. I have an assignment from my physics course. I am from Croatia so i google translated the assignment into English. Please note that I am sorry if this post is little messy, but for some reason I cant use toolbar for complex equations, my browser simply puts ??? in place of symbols.

    1. The problem statement, all variables and given/known data

    Consider the motion of two electrons (without interaction) in a closed nanotube length L=20*10^-9 m, as in the one-dimensional motion of an infinitely high potential pit (solid) walls. If the electrons are described in the single-particle states of the spatial wave functions:
    Y1(x)=Ax^2(x-L) *
    Y2(x)=By(y-L)^2 *


    1) State wave function of electrons with total spin h, and spin projection equal to Oz +h. **
    2) The probability that both electrons are found in the area in this state
    3) Average energy of electrons in this state

    * Y = Psi
    * *reduced planck constant h/2*pi = 1.05457168*10^-34 Js

    (Note: The constants A and B determined from the conditions of standardization)

    2. Relevant equations

    The constants A and B are determined from the conditions of standardization
    P=integral(from 0 to L) |Y(x)dx|^2=1

    I got A=B=sqrt(105)/L^(7/2)

    3. The attempt at a solution

    I have to determine the spatial wave function. Does the spatial wave function of two electrons (or single) must be asymmetric or not? If it has to (and i have used that assumption), then the solution follows:


    sqrt(105)/L^(7/2) * (x^3*y*L^2 - x^3*y^2*L - x^2*y*L^3 - x^2*y^3*L - x*y^3*L^2 +x*y^2*L^3)

    2) That probability is double integral dxdy from sqrt(105)/L^(7/2) * (x^3*y*L^2 - x^3*y^2*L - x^2*y*L^3 - x^2*y^3*L - x*y^3*L^2 +x*y^2*L^3) squared, with borders from L/4 to L.

    2) The equation is quite long, and i think not important right now..

    The problem

    The problem is that I got 0 as a solution to 2), and that isn't the right answer. That probability can't be 0, so i know i did something wrong here. If somebody can help me understand what did I do wrong, that would be great.

    Thank You in advance for help.

    edit: here is the image of all equations
    Last edited: Jun 23, 2012
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted