Difference between revisions of "Quantum Qual Problems"

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1.) Given a quantum mechanical particle of mass <math>M</math> confined inside a box of sides <math>a,b,c</math>.  The particle is allowed to move freely between <math>0 x < a, 0< y< b </math> and <math>0<z<c</math>.
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1.) Given a quantum mechanical particle of mass <math>M</math> confined inside a box of sides <math>a,b,c</math>.  The particle is allowed to move freely between <math>0 <x < a, 0< y< b </math> and <math>0<z<c</math>.
  
 
* Use the time-independent Schrodinger equation for this problem to obtain the general form for the eigenfunctions of the particle
 
* Use the time-independent Schrodinger equation for this problem to obtain the general form for the eigenfunctions of the particle

Revision as of 23:20, 14 August 2007

1.) Given a quantum mechanical particle of mass [math]M[/math] confined inside a box of sides [math]a,b,c[/math]. The particle is allowed to move freely between [math]0 \lt x \lt a, 0\lt y\lt b [/math] and [math]0\lt z\lt c[/math].

  • Use the time-independent Schrodinger equation for this problem to obtain the general form for the eigenfunctions of the particle
  • Now apply boundary conditions to obtain the specific eigenfunctions and eigenenergies for this specific problem.
  • Assume [math]a=b=c[/math] and find the first 6 eigenenergies of the problem in terms of the box side length ([math]a[/math]), the particle mass ([math]M[/math]) and standard constants. What are their quantum number? Make a sketch of the eigenvalue spectrum, a table listing these eigenenergies and the quantum numbers of all the states that correspond to them.


Solution:


2.)