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I need to check my ideas

  1. Dec 28, 2016 #1
    • New poster has been reminded to use the Homework Help Template and post just one question per thread.
    Hello every body i have two problems and i need a help from you

    the problems are attached as a photo
    these two problems about wkb method

    1) at the first one i am confused some thing about the potential when x>0
    what i did i studied the case when x<0 and take my turning points to be (negative infinity and 0) which also some thing confusing me but this is what i can do(if it wrong please correct it) now when the particle is going to positive x is it will feel a barrier potential even the potential is positive and energy is -ve if the answer is yes then i need a help to complete the solution

    also i want a help for taking the turning point i think it when the energy equal the potential but i think this is not consist with what i see in most problems on tunneling

    2) at second problem i divide it to two regions the at 1st region take turning point at (-x/v0 and 0)and 2nd case when x>0 i take turning point (0,x/vo) then make two integration is it correct or no ?
     

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  3. Dec 28, 2016 #2

    BvU

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    Hi there,
    First of all you need to not erase the homework template. List the relevant equations, make clear what variables you use, etc.
    Then post your working.
     
  4. Dec 28, 2016 #3
    Ok .. really iam sorry .. should i edit the post ?
     
  5. Dec 28, 2016 #4

    BvU

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    I'm not a mentor, so personally I'm fine. Point is I don't know where you are running into problems. Is the essence of the wkb method clear ? So what equation do you set up ?
     
  6. Dec 28, 2016 #5
    this is what i did at first problem .. and i cant complete .. please also if you may help me how to determine turning points in such cases ..
     

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  7. Dec 28, 2016 #6

    BvU

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    I'm getting tired of opening the problem description, so:
    Problem statement
    Use the wkb approximation estimate the transition coefficient of a particle of mass m and energy E (E<0) moving in the barrier $$V(x) = -V_0\ \ (x < 0) \quad V(x) = ax^{1/2} \ \ (x \ge 0)$$where a is a positive real constant.

    (That wasn't so hard! Much harder to decipher your handwritten solution attempt)​

    Do I know what a transition coefficient is in this context ? Can I assume the exercise composer means transmission coefficient ? But there is no question of transmission, only some penetration....

    ## - V_0 < E < 0## with time independent SE solution ##e^{ikx} ##. Classical turning point is ##x = 0## Case ##a=0## can be done analytically. Been there, done that ?

    Now what if ##a > 0## but still a small disturbance ? WKB ! Meaning: ...
     
  8. Dec 28, 2016 #7
    sorry for bad handwriting (i made it so quickly )
    yes you could assume that we want transmission coefficient
    Ok if there a small penetration this may assumed to be transmission ,, we find transmission coefficient to determine the probability of such penetration
     
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