(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

THIS IS THE QUESTION

V (x) = [itex]\sqrt{((h-bar ^{2})V_{0})/2m}[/itex] [[itex]\delta(x-a)[/itex]+ [itex]\delta(x+a)[/itex]]

-How do I find R and T?

-Under what condition is there resonant transmission?

2. The attempt at a solution

ok. I got these answers. Are these correct? Someone please tell me.

General Equations

[itex]U_{I}[/itex] = [itex]e^{ikx}[/itex] + R [itex]e^{-ikx}[/itex]

[itex]U_{II}[/itex] = A [itex]e^{ikx}[/itex] + B [itex]e^{-ikx}[/itex]

[itex]U_{III}[/itex] =T [itex]e^{-ikx}[/itex]

Boundary Conditions

if a = 0

[itex]U_{I}[/itex] = [itex]U_{II}[/itex]

1 + R = A + B

[itex]U_{II}[/itex] = [itex]U_{III}[/itex]

A + B = T

discontinuity equation

[itex]U'_{I}[/itex] - [itex]U'_{II}[/itex] = - [itex]\sqrt{\frac{2m V_{o}}{h-bar^{2}}}[/itex] [itex]U_{a}[/itex]

ik (1 - R) - ik (A - B) = - [itex]\sqrt{\frac{2m V_{o}}{h-bar^{2}}}[/itex] R

[itex]U'_{II}[/itex] - [itex]U'_{III}[/itex] = - [itex]\sqrt{\frac{2m V_{o}}{h-bar^{2}}}[/itex][itex]U_{a}[/itex]

ik (A-B) - ikT = - [itex]\sqrt{\frac{2m V_{o}}{h-bar^{2}}}[/itex] T

/// i hope someone can tell me if these are correct so I can continue my calculations. Thanks.

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