Hey there! Sign in to join this conversationNew here? Join for free

The Potential Step - Quantum Mechanics (Additional steps in between needed)? Watch

    • Thread Starter
    Offline

    14
    ReputationRep:
    So, I only got 5/7 for this question and I'm not sure where and what the additional steps in between this solution is needed.Name:  1.jpg
Views: 31
Size:  263.2 KB*Attachment 585736585740*Attachment 585736585740585700
    Attached Images
      
    Offline

    11
    ReputationRep:
    (Original post by Airess3)
    So, I only got 5/7 for this question and I'm not sure where and what the additional steps in between this solution is needed.Name:  1.jpg
Views: 31
Size:  263.2 KB*Attachment 585736585740*Attachment 585736585740585700
    I guess that it is because you did not show the working of how you combine the two continuity equations meaning solving the two simultaneous equations to obtain T and R respectively.
    It may also be good that make all your workings explicit in future unless you are told by your lecturer otherwise.
    Hope it helps.
    • Thread Starter
    Offline

    14
    ReputationRep:
    (Original post by Eimmanuel)
    I guess that it is because you did not show the working of how you combine the two continuity equations meaning solving the two simultaneous equations to obtain T and R respectively.
    It may also be good that make all your workings explicit in future unless you are told by your lecturer otherwise.
    Hope it helps.
    Thanks. Could also explain the (matching psi) and *(matching derivative of psi) part of my answer? I copied that from the board and when I looked back on it, I didn't quite understand how it related to the question.
    Offline

    11
    ReputationRep:
    (Original post by Airess3)
    Thanks. Could also explain the (matching psi) and *(matching derivative of psi) part of my answer? I copied that from the board and when I looked back on it, I didn't quite understand how it related to the question.
    I don't quite understand your question.

    Hope the following would help:

    Matching the wavefunction at x = 0:

    wavefunction in A = wavefunction in B

     \psi_A(0) = \psi_B (0)

     \exp( ik(0)) + R \exp(-ik(0)) = T\exp( iq(0))

    Matching the derivative of wavefunction at x = 0:

    derivative of wavefunction in A = derivative of wavefunction in B

     \[{{\left. \frac{d}{dx}{{\psi }_{A}} \right|}_{x=0}}\] =\[{{\left. \frac{d}{dx}{{\psi }_{B}} \right|}_{x=0}}\]

     ik \left( \exp( ik(0)) - R \exp(-ik(0))) \right ) =  iqT\exp( iq(0))

    Imposing these conditions allow us to have a smooth wavefunction.
    • Thread Starter
    Offline

    14
    ReputationRep:
    (Original post by Eimmanuel)
    I don't quite understand your question.

    Hope the following would help:

    Matching the wavefunction at x = 0:

    wavefunction in A = wavefunction in B

     \psi_A(0) = \psi_B (0)

     \exp( ik(0)) + R \exp(-ik(0)) = T\exp( iq(0))

    Matching the derivative of wavefunction at x = 0:

    derivative of wavefunction in A = derivative of wavefunction in B

     \[{{\left. \frac{d}{dx}{{\psi }_{A}} \right|}_{x=0}}\] =\[{{\left. \frac{d}{dx}{{\psi }_{B}} \right|}_{x=0}}\]

     ik \left( \exp( ik(0)) - R \exp(-ik(0))) \right ) =  iqT\exp( iq(0))

    Imposing these conditions allow us to have a smooth wavefunction.
    Thanks.
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Has a teacher ever helped you cheat?
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • 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

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