- #1
alewisGB
- 15
- 0
Homework Statement
before a potential barrier show;
ψ(x) = B*sin(kx-∅)
B, k and ∅ are all possitive
Is a solution of the one dimensional Schroedinger equation
Homework Equations
ψ(x) = B*sin(kx-∅)
Eψ(x) = -(ħ2/2m)(d2ψ(x)/dx2)+U(x)ψ(x)
The Attempt at a Solution
If it is before the barrier U(x) = 0 so;
Eψ(x) = -(ħ2/2m)(d2ψ(x)/dx2)
ψ(x) = B*sin(kx-∅)
dψ(x)/dx= Bk*cos(kx-∅)
(d2ψ(x)/dx2) = -Bk2*sin(kx-∅)
By substitution;
E = ħ22k2/2m
λ = h/p (de broglie wavelength)
p = mv
h = λmv
so k = 2π√(2Em) / λmv
??
apparently I should get;
k=2π/λ
What I have is a multiple of 2π/λ
What have I done wrong / what else should I do
Thanks in advance for and help you offer