Consider a particle moving along the x-axis and constrained within -pi/2 < x < p

Question

Consider a particle moving along the x-axis and constrained within -pi/2 < x < pi/2 The particle can be described by a wave function equal to Acos(x) for -pi/2 < x < pi/2
a) calculate the normalization constant A
b) calculate the expectation value <x>. hint: use symmetry arguments
c) what conditions should a proper wave function satisfy?
d) write down the wave function of the particle at x greater than or equal to pi/2
e) derive the expression for the ground state energy of the particle in a box at -pi/2 < x < pi/2 Hint: you can derive the expression by using either the time-independent schrodinger equation and the wave function corresponding to the ground state or the expression for the energy levels of a particle in a box.

Explanation / Answer

(x)=Acosx

a)

(-/2./2)|(x)|2dx=1   =>A2(-/2./2)cos2x.dx

=>A2/2.(-/2./2)(1+cos2x)dx

=.A2/2=1

A=(2/)

b)<x>=0

c)(x) continues,normalised,finite when:

x->(+,-),single valued

=>'(x) continues if |U(x)|< every where

d)(x)=0

e)E=h2/2m

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.