Solving WKB Method Problems with Confusing Potential and Turning Points

[physicist 12345]

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 ?

 

[BvU]

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.

 

[physicist 12345]

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.

Ok .. really iam sorry .. should i edit the post ?

 

[BvU]

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 ?

 

[physicist 12345]

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 ?

this is what i did at first problem .. and i can't complete .. please also if you may help me how to determine turning points in such cases ..

 

[BvU]

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: ...

 

[physicist 12345]

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: ...

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