 #1
Theodore0101
 10
 0
 Homework Statement:

A particle with mass m is effected by potential V(x) = ∞ when x<0, V0 when 0<x<a, 0 when x>a
A) Set up a relation from which the energy for bounded states can de determined
B) For which values V0 does the particle have only one bounded state?
 Relevant Equations:
 tan(√(2ma^2(E+V0)/h^2)=√(E+V0/E)
Homework Statement:: A particle with mass m is effected by potential V(x) = ∞ when x<0, V0 when 0<x<a, 0 when x>a
A) Set up a relation from which the energy for bounded states can de determined
B) For which values V0 does the particle have only one bounded state?
Homework Equations:: tan(√(2ma^2(E+V0)/h^2)=√(E+V0/E)
Hi! I understand the most of this example problem, I have no problem with A), which the answer is the relation tan(√(2ma^2(E+V0)/h^2)=√(E+V0/E), and I mostly understand B), it is just one part in the end I can't follow. Choosing the tangens function so that it only has one period in the corresponding intervall V0<E<0 and the equations only have one point that they meet in. Therefor we put that pi/2 < √(2ma^2(E+V0)/h^2) <3pi/2 since pi/2 to 3pi/2 is a period for a tangens function, but from there they say that the equation gives pi^2*h^2/8ma^2 < V0 < 9pi^2*h^2/8ma^2, but I don't follow this step. What happened to E, why are you allowed to take it away? Shouldn't it be pi^2*h^2/8ma^2 < V0 + E < 9pi^2*h^2/8ma^2 (instead of just V0)?
Thanks
A) Set up a relation from which the energy for bounded states can de determined
B) For which values V0 does the particle have only one bounded state?
Homework Equations:: tan(√(2ma^2(E+V0)/h^2)=√(E+V0/E)
Hi! I understand the most of this example problem, I have no problem with A), which the answer is the relation tan(√(2ma^2(E+V0)/h^2)=√(E+V0/E), and I mostly understand B), it is just one part in the end I can't follow. Choosing the tangens function so that it only has one period in the corresponding intervall V0<E<0 and the equations only have one point that they meet in. Therefor we put that pi/2 < √(2ma^2(E+V0)/h^2) <3pi/2 since pi/2 to 3pi/2 is a period for a tangens function, but from there they say that the equation gives pi^2*h^2/8ma^2 < V0 < 9pi^2*h^2/8ma^2, but I don't follow this step. What happened to E, why are you allowed to take it away? Shouldn't it be pi^2*h^2/8ma^2 < V0 + E < 9pi^2*h^2/8ma^2 (instead of just V0)?
Thanks