Register to reply

Probability current inside the barrier of a finitie square potential well

Share this thread:
StephenD420
#1
Feb26-12, 03:45 AM
P: 100
if ψ=C*e^(kx) + D*e^(-kx)
show that the probability current density is
Jx=(i*k*hbar/m)[c*conj(D) - conj(C)*D]

since Jx= (i*hbar/2m)*[ψ * derivative of conj(ψ) - conj(ψ)*derivative of ψ]
ψ=C*e^(kx) + D*e^(-kx)
conj(ψ)= conj(C)*e^(-kx) + conj(D)*e^(kx)
ψ ' = C*k*e^(kx) - D*K*e^(-kx)
derivative of conj(ψ) = -conj(C)*k*e^(-kx) + conj(D) *k*e^(kx)

plugging in and simplifying I get

Jx = (i*hbar/2m)*[-C*conj(C)*k - k*conj(C)*D*e^(-2kx) + C*conj(D)*k*e^(2kx) + D*conj(D)*k -C*conj(C)*k -C*conj(D)*k*e^(2kx) + conj(C)*D*k*e^(-2kx) +D*conj(D)*k]

which simplifies to
Jx = (i*hbar/2m)*[-2*c*conj(C)*k + 2*D*conj(D)*k]
Jx = (i*hbar/m)*[D*conj(D) - C*conj(C)]

how do I get from here to
Jx=(i*k*hbar/m)[c*conj(D) - conj(C)*D]

Thanks so much for any help you guys can provide. I am really stuck as to what to do next.
Thanks.
Stephen
Phys.Org News Partner Science news on Phys.org
Security CTO to detail Android Fake ID flaw at Black Hat
Huge waves measured for first time in Arctic Ocean
Mysterious molecules in space
StephenD420
#2
Feb27-12, 12:53 AM
P: 100
bump....
Please help me with a nudge to finish this problem up.

Thank you for any help you guys can give me. I really appreciate it.
Stephen


Register to reply

Related Discussions
Square potential barrier, normalization Quantum Physics 0
Probability inside finite square well Introductory Physics Homework 2
Potential barrier inside an infinite well: Should the amplitude be the same both side Advanced Physics Homework 5
What exactly is barrier tunneling and potential barrier? Quantum Physics 6
Potential barrier, wave function, and probability... Quantum Physics 0