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: 1 Dimentional Schrodinger equation

  1. Oct 14, 2012 #1
    1. The problem statement, all variables and given/known data
    Consider the one dimensional wave funciton give below.
    a) Draw a graph of the wave function for the region defined.
    b) Determine the value of the normalization constant
    c) what is the probability of finding the particle between x = 0 and x = a/2
    d) show that the wave fucntion is a solution of the non-relativistic wave equation (Schrodinger equation) for the potential energy function give below.
    ψ(x) = A(a^2-x^2) for -a < x < +a
    ψ(x) = 0 for x< -a and x > a
    U(x) = -((h bar)^2/ma^2)(x^2/(a^2-x^2))

    2. Relevant equations
    shown above

    3. The attempt at a solution
    a)
    JK7Qe.png

    b)

    a
    ∫ ψ(x)^2 dx =1
    -a

    a
    ∫ (A(a^2-x^2))^2 dx = 1
    -a

    A = (√15 )/4√a^5

    c)
    39.4%

    d)


    I was given the question without answer, some help verifying my answer would be appreciated!!
     
    Last edited: Oct 14, 2012
  2. jcsd
  3. Oct 14, 2012 #2
    for part d, do I just do this?:
    Meyxo.jpg
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...
Similar Threads for Dimentional Schrodinger equation Date
Showing that a wavefunction can be written as a product Nov 21, 2016
Dynamics in two dimentions Mar 26, 2015
One Dimentional Relative Motion Sep 11, 2013
Motion in two dimention problem Nov 15, 2012
Dimentional Anaylsis: Solving for Revolutions Sep 2, 2012