Quantum Qual Problems: Difference between revisions
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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>. | 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]\displaystyle{ M }[/math] confined inside a box of sides [math]\displaystyle{ a,b,c }[/math]. The particle is allowed to move freely between [math]\displaystyle{ 0 <x < a, 0< y< b }[/math] and [math]\displaystyle{ 0<z<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]\displaystyle{ a=b=c }[/math] and find the first 6 eigenenergies of the problem in terms of the box side length ([math]\displaystyle{ a }[/math]), the particle mass ([math]\displaystyle{ 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.)