Quantum Oscillator

  • #1

Homework Statement


Problem 8.
1. Express the distance [tex]x_c[/tex] as a function of the mass [tex]m[/tex] and the restoring
parameter [tex]c[/tex] used in Problem 7.

(Problem 7.
1. Calculate the energy of a particle subject to the potential [tex]V(x) = V_0 +
cx^2/2[/tex] if the particle is in the third excited state.
2. Calculate the energy eigenvalues for a particle moving in the potential
[tex]V(x) = cx^2/2 + bx[/tex].)

Quantum Mechanic. Chapter 3. Daniel B. Res.


Homework Equations



[tex]H=\frac{p^2}{2m}+\frac{m\omega ^2}{2}x^2[/tex]


The Attempt at a Solution


I cannot understand what is actually meant by this parameter [tex]x_c[/tex] and how to approach the problem.
 

Answers and Replies

  • #2
vela
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It might help if you provided the complete problem statement for problem 8. The reference to problem 7 just means c is a spring constant; it doesn't say anything about what xc is supposed to represent.
 
  • #3
Problem 8.
1. Express the distance [tex]x_c[/tex] as a function of the mass [tex]m[/tex] and the restoring
parameter [tex]c[/tex] used in Problem 7.
2. If [tex]c[/tex] is multiplied by 9, what is the separation between consecutive eigenvalues?
3. Show that [tex]x_c[/tex] is the maximum displacement of a classical particle moving
in a harmonic oscillator potential with an energy of [tex]\hbar\omega/2[/tex].
 
  • #4
vela
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Well, your confusion is understandable if this is all the info you have. I have no idea how xc is defined either.
 

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