One dimensional Schroedinger equation solution

[alewisGB]

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

 

[alewisGB]

E = 0.5 * m * v^2 I got it :)