Modern Quantum Mechanics (QM2) —— Introduction

For my nearly-diaqualified QM1 exam and imperfect tomorrow.

Future may collapse, path to target might wax and wane, but be convinced that ultimate harvest is worthy of endeavour. ——Preface

In this series, I might attempt to write my study notes totally by English, an enormous challenge to myself. If you find any mistake about grammar/explanation/comprehension/..., please feel free to contact me.

Distinguished from Quantum Mechanics (QM1) and Advanced Quantum Mechanics (AQM), Modern Quantum Mechanics (MQM, or QM2) can be valued as a briging curriculum between undergrates and postgraduates. As we know, constructed by several essential hypotheses, QM1 embrace vital principles and theorems, including wave function normalization, potential wall, Dirac notation, angular momentum coupling, perturbation theory and so on. On this foundation, QM2 will focus on more comprehensive quantization problems, which may involve Theoretical Mechanics, Electrodynamics, Thermaldynamics,etc., intending to provide a idiomatic transition to advanced courses for sophomore and junior.

Comprised of 14 chapters, QM2 begins with summary and disciplines of QM1, then discusses the movement of charged particles in electromagnetic field with a more "quantized" horizon——regards particles as a wave function instead of a mass, and assume the velocity of particles is extermely high(close to lightspeed). Next, we pull in Heisenberg's picture and its classic correspondence, which correlates to Landau energy level and Landau gauge. Combined with Classical Electrodynamics, we discuss quantized interpretation of Hall effect, drawing forth semi-quantum hall effect. In addition, magnetic monopole, Anaronov-Bohm effect, composite system, ensembles and path integral quantization will be interpreted. Finally, we step into relativistic quantum mechanics, coping with problems with higher dimensions.

This series will undoubtedly keep updating, but owing to personal arrangement for my Postgraduate Entrance Exam(PEE) in the upcoming December, the frequency of updating is uncertain. I apologize for any inconvenience caused, and I cordially anticipate that you can keep in contact with this series. Both commenting and private chatting are welcome.

By the way, maybe you're able to calculate the uncertainty of my updating frequency, just take my every blog as quantized, then start with a normalized wave function...(Obviously I'm joking :)

See you in next blog!

References for QM2 courses are as follows:

[1] J.J.Sakurai, Modern Quantum Mechanics, World Book Publishing Co.

[2]N. Nagaosa, Quantum Field Theory in Condensed Matter Physics.

[3]Y.V.Nazarov, J.Danon. Advanced Quantum Mechanics, Cambridge Press.

[4]曾谨言.量子力学卷II.科学出版社.