- #1
kehler
- 104
- 0
Homework Statement
Show whether the functions
psi_I = A cos(kx - wt)
psi_II = A sin(kx - wt)
are solutions of Schrodinger equation for a free particle
Homework Equations
Schrodinger equation
The Attempt at a Solution
For psi_I = A cos(kx - wt),
d2psi_I/dx2 = -Ak2psi[/SUB]I[/SUB]
dpsi_I/dt = Awsin(kx - wt)
Substituting into S.E,
ih_bar Awsin(kx - wt) = ((h_bar)2/2m) Ak2psi_I + 0 psi (free particle so V=O)
So it doesn't satisfy the S.E.
For psi_II = A sin(kx - wt),
d2psi_II/dx2 = -Ak2psi[/SUB]II[/SUB]
dpsi_II/dt = -Awcos(kx - wt)
Substituting into S.E,
ih_bar -Awcos(kx - wt) = ((h_bar)2/2m) Ak2psi_II + 0 psi
So it doesn't satisfy the S.E either.
Is this correct? Or is there some way that I'm supposed to manipulate both sides to equal each other? :S