- #1
Haxx0rm4ster
- 37
- 0
When solving Schrodinger's eqn for a quantum ring, what would be the boundary conditions?
The solution (polar) should be
Ψ(Φ) = A exp(ikΦ) + B exp(-ikΦ)
And I believe the boundary conditions are
Ψ(0) = Ψ(2pi)
Ψ(0) = A + B
Ψ(2pi) = A exp(ik*2π) + B exp(ik*2π)
and I suppose I can safely say that
Ψ(0) = 0
From these conditions/assumptions,
k = n, n = 1,2,3...
B = -A,
And therefore
Ψ(Φ) = A exp(inΦ) - A exp(-inΦ)
Which can be expressed as
Ψ(Φ) = 2Ai sin(nΦ)
I'm just wondering, are my boundary condition assumptions complete and correct?
Thanks
The solution (polar) should be
Ψ(Φ) = A exp(ikΦ) + B exp(-ikΦ)
And I believe the boundary conditions are
Ψ(0) = Ψ(2pi)
Ψ(0) = A + B
Ψ(2pi) = A exp(ik*2π) + B exp(ik*2π)
and I suppose I can safely say that
Ψ(0) = 0
From these conditions/assumptions,
k = n, n = 1,2,3...
B = -A,
And therefore
Ψ(Φ) = A exp(inΦ) - A exp(-inΦ)
Which can be expressed as
Ψ(Φ) = 2Ai sin(nΦ)
I'm just wondering, are my boundary condition assumptions complete and correct?
Thanks