# Quantum mechanics

if you know the wave ...
how do you determine the reflected and transmitted waves?

the book tells you to enforce the required continuity conditions to obtain their (possibly complex) amplitudes

ZapperZ
Staff Emeritus
sweetvirgogirl said:
if you know the wave ...
how do you determine the reflected and transmitted waves?
the book tells you to enforce the required continuity conditions to obtain their (possibly complex) amplitudes
You cannot expect a coherent answer when you ask something this vague.

Zz.

As vague as that question is, I think the answer you are looking for is that:

Y= Psi because I dont know how the nifty regulars use that fancy font
Yi: Incident wave
Yr: Reflected wave
Yt: Transmitted wave
Y': Derivative of wave equations with respect to position (x)

Lets assume that the potential barrier is at x = a
you have two continuity equations

Yi(a) + Yr(a) = Yt(a)
Yi'(a) + Yr'(a) = Yt'(a)

I doubt that answers your question since im not sure what it is, but you can figure everything out from these continuity equations.

elhinnaw said:
As vague as that question is, I think the answer you are looking for is that:
Y= Psi because I dont know how the nifty regulars use that fancy font
Yi: Incident wave
Yr: Reflected wave
Yt: Transmitted wave
Y': Derivative of wave equations with respect to position (x)
Lets assume that the potential barrier is at x = a
you have two continuity equations
Yi(a) + Yr(a) = Yt(a)
Yi'(a) + Yr'(a) = Yt'(a)
I doubt that answers your question since im not sure what it is, but you can figure everything out from these continuity equations.
Let me type the exact q ...

A beam of particles of energy E and incident upon a potential step of U0 = 3/4 E is described bby the wae funciton
Y(x) = 1 e^(ikx)
The amplitude of the wave (related to the number incident per unit distance) is arbitrarily chosen as unity.
a) Determine completely the reflected and transmitted waves by enforcing the required continuity conditions to obtain their (possibly comlex) amplitudes
b) Verify that the ratio of reflected probability desnity to the incident probability desnity agrees with
the equation ... T = .... R = ....

what i dont get is what the hell is "required continuity conditions"

The wavefunction and it's derivative must be continuous at the barrier's edge.

Gokul43201
Staff Emeritus
Gold Member
inha said:
The wavefunction and it's derivative must be continuous at the barrier's edge.
...which is a specific part of the requirement that the wavefunction be continuously derivable EVERYWHERE.

Fermat
Homework Helper
elhinnaw said:
...
Y= Psi because I dont know how the nifty regulars use that fancy font
....
You can use https://www.physicsforums.com/misc/howtolatex.pdf" [Broken] from where you can copy and paste individual characters.

Last edited by a moderator:
lightgrav
Homework Helper
wave function derivatives

Gokul43201 said:
...which is a specific part of the requirement that the wavefunction be continuously derivable EVERYWHERE.
Gokul, with step functions, delta-functions, and linear-cusp functions being commonplace portions of model potentials, that was a VERY misleading thing to say.:yuck:
If the Potential is smooth, then the wave function will be also;
If the Potential has infinities, jumps, or kinks, then the wave function
will have discontinuous 1st, 2nd, or 3rd derivitives ...
otherwise the equation isn't satisfied.