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 | |
| − | + | * 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: | #* Solution: | ||
Revision as of 22:54, 14 August 2007
- Problem: Given a quantum mechanical particle of mass confined inside a box of sides . The particle is allowed to move freely between and .
- 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 and find the first 6 eigenenergies of the problem in terms of the box side length (), the particle mass () and standard constants. What are their quantum number?
- Solution: