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!

Q.M. harmonic oscillator spring constant goes to zero at t=0

  1. Sep 25, 2013 #1
    1. The problem statement, all variables and given/known data

    A one-dimensional harmonic oscillator is in the ground state. At t=0, the spring is cut. Find the wave-function with respect to space and time (ψ(x,t)).

    Note: At t=0 the spring constant (k) is reduced to zero.

    So, my question is mostly conceptual. Since the spring constant goes to zero at t=0 is it safe to assume that the problem can now be considered as a free particle problem since the potential goes to zero when 'k' goes to zero?

    If this assumption is correct I should be able to solve the time independent Schrodinger equation, ψ(x,0), then multiply in the time part and solve for the constant.

    I do not see how being a harmonic oscillator will affect my answer since once you cut the spring it is no longer a harmonic oscillator.

    Is there something I am missing conceptually?
  2. jcsd
  3. Sep 25, 2013 #2


    User Avatar
    Homework Helper
    Gold Member
    2017 Award

    Hello FarticleFysics and welcome to Physics Forums!

    Yes, the particle instantaneously becomes free at t = 0. But the wavefunction does not undergo any instantaneous change at t = 0.

    ##\psi(x, 0^+)## = ##\psi(x, 0^-)##

    The wavefunction at time t = 0 will not be a solution of the time independent Schrodinger equation for a free particle. But the wavefunction at t = 0 may be expanded as a superposition of solutions of the time independent, free-particle Schrodinger equation. You can then put in a time dependent factor for each member of the superposition.

    The harmonic oscillator potential can be thought of as "preparing" the quantum state of the particle at time t = 0.
    Last edited: Sep 25, 2013
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted