Previous lecture 2010.11.02                                    to index                                Next lecture 2010.11.16     

Quantizing extended system,                                  04.11.2010
Creation+Annihilation Operators,
Density of states

Included below: Lagrange function and Hamilton function for a charged particle in el mag field
charge-in-elmag-derivation-jpg/ Here are preliminary pictures of pages ....


1-quantum-theory-of-extended-systems.png

---

Classical mechanics - Finding eigenmodes


2-eigenmodes-of-coupled-oscillating...png

---

3-eigenmodes-of-coupled-oscillating...png

---

Quantum mechanics - for each independent Harmonic Oscillator

5-QM-harm-oscillator.png

---

EXTRA BONUS:  Solve Schrödinger Equation as a 1. order equation - see below
6-extra-QM-harm-oscillator.png

---

7-Fields.png

---

Electro-magnetic fields;  ENERGY
a1-energy-inmagn-field.png

---

Quantization of El-Mag Field
a2-field-energy-QM.png

---

a3-field.png

---

Lagrange function and Hamilton function for a charged particle in el mag field
charge-in-elmag-derivation-jpg/ Here are preliminary pictures of pages ....
a4-doing_particle_in_elmag.png

---

Density of states   -  Continuum energies - Quasicontinuum derivations

b1-density-of-states.png

---

b1-f-density-of-states.png

---

b2-density-of-states.png

---

b2-n-factors-density-of-states.png

---

b3-sum_1_over_delta_sum_delta.png   (Both picture and text from PHYS208 Lecture)

The colored "expression" can be anything in the sum (integral) above

The argumet goes like this:
   sum    ->  sum  with the proper deltas which are compensated by the 1/Deltas outside the sum
 
Then  keep the 1/Deltas outside the sum 
 and concentrate on the Sum with deltas;   Taking this by itself, it will converge to an integral
                                                                    when you make Deltas infinitesimal
The Deltas outside are not to be made infinitesimal, SINCE they connect to the original sum

This is sometimes not so easy to keep in mind ....  ( the sum itself would go to infinity ... )

From this follows the dependence of Fermi energy on N/V - the density (see last time ... )

---

FINAL RESULT - Discussion
ee.png

---

ff-stimulated_emission.png

---

Previous lecture 2010.11.02                              to index                                       Next lecture 2010.11.16              

---