Advanced Solid State Physics

Quantization

• Recipe for quantization
• Construct the Lagrangian by inspection
• Differentiate the Lagragian to find the conjugate variables
• Use the conjugate variables to perform a Legendre transformation from the Lagrangian to the Hamiltonian
• Examples
• LC circuit
• Transmission line
• Dissipation in quantum mechanics
• Wave equation      W
• Electrons in a magnetic field

Resources
• The quantization of the wave equation is discussed in appendix C of Kittel and the quantization of electrons in a magnetic field is discussed in Appendix G of Kittel.
• Some notes on the correspondence principle, Elisabeth Rogl, 2014.