Quantum QM Textbooks (Education + Research purposes)

[phys_enthusiast_001]

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!

 

[The Bill]

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.

 

[vanhees71]

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.

 

[phys_enthusiast_001]

Alright I appreciate the responses both of you. I might possibly get 3 textbooks instead of 2 by the look of things hmmm