Advanced Solid State Physics

Advanced Solid State Physics Version 2009: Michael Mayrhofer-R., Patrick Kraus, Christoph Heil, Hannes Brandner, Nicola Schlatte ...

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1 What is Solid State Physics 2 Schrödinger Equation 3 Quantization 3.1 Quantization 3.1.1 Quantization of the Harmonic Oscilla ...

1 What is Solid State Physics Solid state physics is (still) the study of how atoms arrange themselves into solids and what prop ...

2 Schrödinger Equation The framework of most solid state physics theory is theSchrödinger equationof non relativistic quantum me ...

3 Quantization The first topic in this chapter is the appearance ofRabi oscillations. For understanding their origin a few examp ...

wavefunction doesn’t vanish completelyon the other side! There is a small probability for the nitrogen atom to tunnel through th ...

3.1 Quantization For the quantization of a given system withwell defined equations of motionit is necessary to guess a Lagrangia ...

3.1.1 Quantization of the Harmonic Oscillator The first example how a given system can be quantized is a one dimensional harmoni ...

Figure 3: Superconducting ring with a capacitor parallel to a Josephson junction 3.1.2 Quantization of the Magnetic Flux The nex ...

The conjugate variable is ∂L ∂Φ ̇ =CΦ = ̇ Q. Then the Hamiltonian via a Legendre transformation: H=QΦ ̇−L= Q^2 2 C + (Φ−Φe)^2 2 ...

The conjugated variable to position has now two components, the first therm in eqn.(9)mvwhich is the normal momentum. The second ...

|Ψ〉=|ψSpace〉⊗|χSpin〉 Where the Symbol⊗denotes a so called tensor product. The Schroedinger equation reads (Hˆ 1 ⊗‖ˆ+Sˆ⊗ˆ‖)|ψSpac ...

By completing the square we get a term−~^2 ky^2 which cancels with the one already there and we are left with 1 2 m (−~^2 φ′′+~^ ...

4 Quantization of the Electromagnetic Field - Quantization Recipe This chapter serves as a template for the quantization of phon ...

Aas the amplitude of the plane wave, with a linear dispersion relationship (still classical) of ω=c|k|. To quantize the wave equ ...

To get some macroscopic properties the partition function is useful, especially the canonical partition functionZ(T,V) Z(T,V) = ...

Figure 4: Quantization of k-space For further analysis the sum is converted to an integral. Before this can be done, thedensity ...