QM Textbooks (Education + Research purposes)

In summary, a physicist is looking for two quantum mechanics textbooks to help with their research. The aim of the research is to search for new particles, using atomic and molecular experiments, test of Grand Unification theories and search for Dark matter. The relevant experience for the physicist includes having completed a second year undergraduate course in quantum physics. The experience that is missing for the physicist is mathematical knowledge.
  • #1
phys_enthusiast_001
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Hello fellow physics enthusiasts!
Apologies in advance, I wanted to make the most out of this post and so it ended up being quite long + detailed. I thank you for your patience and any efforts to help!

What I'm looking for:
TWO good Quantum Mechanics textbooks for the rest of my undergraduate and postgraduate studies - textbooks are expensive investments! I want to make sure I get the right ones for me. As an additional requirement it should have the following (whether independently or separately):
  • Dirac equation
  • Relativistic Schrodinger Equation
  • Klein-Gordon equation
And this isn't a requirement but more of a preference:
  • Should leave out some derivations for me to do myself but not TOO much of this - I like to do the maths and derivation by myself but this typically takes a lot longer and I am working within time constraints here

Context
I have recently just finished my second year of undergraduate physics. I have already had basic exposure to Quantum Physics through a second year course - although I am not sure "how much" exposure and so there will be a more comprehensive list of what I have learned later on to help you nice people gauge my level of experience.

As part of a scholarship, I will be helping one of the physicists at my university with Dark Matter research. BUT as I only have a 2nd year level understanding of quantum, it is insufficient to be able to help him. And so I will have to learn more quantum by myself off textbooks first.

The aim of the research is to "search for new particles, using atomic and molecular experiments, test of Grand Unification theories and search for Dark matter". As part of my preparation I have been asked to study:
1. Dirac equation
2. Obtain Schrodinger equation from Dirac equation including relativistic corrections
3. Dirac equation in spherical potential, Schrodinger equation in spherical potential
4. Solutions for hydrogen-like ions
5. Klein-Gordon equation

Relevant Experience

Maths:
  • Vector geometry
  • Vector spaces
  • Matrices - eigenvalues/vectors, linear transformations,
  • Statistics - distributions, hypothesis tests, confidence intervals, regression analysis
  • Taylor and Laurent series
  • 1st and 2nd order ODEs
  • Vector calculus - triple integrals, Stoke's, Green's, Gauss'
  • Complex analysis - analytic functions, Cauchy-Riemann, Cauchy Integrals, complex trig exp logs
  • Numerical methods - MATLAB, ODE and PDE numerical solutions
Physics:
  • Classical Mechanics - Lagrangian, Hamiltonian, Special Relativity, Oscillations
  • Quantum Physics - Schrodinger, Infinite and Finite Square well, Harmonic oscillator, hydrogen atom, bra-ket notation, operators, commutators, Hermitian matrices, eigenstates, time evolution, Hamiltonian, spins, Paul spin matrices, Bohr-Sommerfeld
  • Electromagnetism - electric and magnetic dipoles, electric potential, magnetic vector potential, free currents, Gauss, Ampere, dielectrics, conductors, magnetic materials, Maxwell
  • Optics - thin films, Fresnel reflection, transfer and propagation matrices, Jones matrices, polarisation
If there may be some mathematical knowledge I am missing, it would also be great to know what.

THANK YOU! for putting up with such a picky student - I just really want 2 textbooks which tailor suit my learning!
 
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  • #2
I don't think there exist any two textbooks which I'd recommend to cover that material the way you want.

If you allow me to recommend three textbooks, though, it'd be the following:

Shankar's Principles of Quantum Mechanics, 2nd ed.
Sakurai and Napolitano's Modern Quantum Mechanics, 2nd ed.
Wachter's Relativistic Quantum Mechanics

If you really pressed me, I suppose you could do with just Shankar and Wachter. However, being able to go back and forth between Shankar and Sakurai for explanations can be quite helpful while learning the fundamentals.
 
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  • #3
You can save some money when not buying a textbook that claims relativistic QT could be treated as non-relativistic QT. The only successful formulation we have today is relativistic QFT. For non-relativistic QT I recommend Sakurai, Modern Quantum Mechanics, and for relativistic QFT M. Schwartz, Quantum Field Theory and the Standard Model.
 
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  • #4
Alright I appreciate the responses both of you. I might possibly get 3 textbooks instead of 2 by the look of things hmmm
 

Related to QM Textbooks (Education + Research purposes)

1. What is QM?

QM, or quantum mechanics, is a branch of physics that studies the behavior of particles at the atomic and subatomic level. It explains how particles interact and how energy and matter behave on a microscopic scale.

2. Why are QM textbooks important for education?

QM textbooks are essential for understanding the fundamental principles of quantum mechanics, which is crucial for students studying physics, chemistry, and other fields that involve understanding the behavior of particles at the atomic level. These textbooks provide a structured and comprehensive approach to learning about QM, with clear explanations and examples to help students grasp complex concepts.

3. Are QM textbooks suitable for research purposes?

Yes, many QM textbooks are written by experts in the field and cover advanced topics and cutting-edge research. These textbooks can serve as valuable resources for researchers in the field of quantum mechanics, providing a comprehensive overview of current theories and experiments.

4. What are some common topics covered in QM textbooks?

Some common topics covered in QM textbooks include wave-particle duality, the uncertainty principle, quantum states and operators, quantum entanglement, and the Schrödinger equation. These topics are essential for understanding the principles of QM and their applications in various fields.

5. Do QM textbooks require a strong background in math?

Yes, QM textbooks often require a strong foundation in mathematics, including calculus, linear algebra, and differential equations. These mathematical concepts are crucial for understanding the complex equations and principles of quantum mechanics. However, some introductory QM textbooks may provide a review of necessary mathematical concepts for those without a strong math background.

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