Difference between revisions of "Quantum Qual Problems"

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# Problem: 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>.
 
# Problem: 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
  
#*  Now apply boundary conditions to obtain the specific eigenfunctions and eigenenergies for this specific problem.
+
*  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?  
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*  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?  
 
#* Solution:
 
#* Solution:

Revision as of 22:54, 14 August 2007

  1. Problem: 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 \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?
    • Solution: