I have a question that's driving me insane and I'm sure there's a simple answer that I'm missing for some reason, but I'm not getting my a-ha moment.(adsbygoogle = window.adsbygoogle || []).push({});

Consider 2 cases from intro QM:

Infinite square well

Potential barrier with E > V_{0}

For the infinite square well, the Schrodinger eqn gives

d2ψ/dx2 + k^{2}ψ = 0

Since k^{2}> 0, this gives oscillating solutions (some combination of sines and cosines). Correct?

For the potential barrier with E > V0, the Schrodinger eqn gives (with the potential jumping from 0 to V_{0}at x = 0)

d^{2}ψ/dx^{2}+ k^{2}_{I}E = 0 (where k_{I}= √2mE/(hbar^{2})

prior to the potential step (i.e. for x < 0) and

d^{2}ψ/dx^{2}+ k^{2}_{II}E = 0 (where k_{II}= √2m(E-V0)/(hbar^{2})

after the potential step (for x > 0)

My problem is this: As far as I can tell, both k_{I}and k_{II}are positive numbers (since E > V_{0}> 0). Why, then, do they give non-oscillating solutions? Whereas, for the infinite square well, a positive k gave oscillating solutions?

Am I making a sign error here or just forgetting something from differential equations? What is different about these equations that one of them gives oscillating, and the other non-oscillating, solutions?

Thanks for any help!

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Solving Schrod. Eqn. for Potential Barrier with E > V

Loading...

Similar Threads - Solving Schrod Potential | Date |
---|---|

I Lho potential | Feb 7, 2018 |

I Solving the Schrödinger eqn. by commutation of operators | Jan 8, 2018 |

I Dirac equation solved in Weyl representation | Nov 15, 2017 |

I Solving for <E^2> of a non-stationary state of the QSHO | Jul 14, 2017 |

**Physics Forums - The Fusion of Science and Community**