In: Physics
A particle of mass m is confined to a finite potential energy well of width L. The equations describing the potential are
U=U0 x<0
U=0 0 < x < L
U=U0 x > L
Take a solution to the time-independent Schrodinger equation of energy E (E < U0) to have the form
A exp(-k1 x) + B exp(k1 x) x < 0
C cos(-k2 x) + D sin(k2 x) 0 < x < L
F exp(-k3 x) + G exp(k3 x) x > L
Which of the following statements is not correct for this solution?
C cos(-k2 L) + D sin(k2 L) = F exp(-k3 L)
The wave function is continuous at x=0 and x=L
k_1=sqrt(2m( U0-E ))/hbar
k1=k3
B=0
The first derivative of the wave function is continuous at x=0 and x=L