Primer of Quantum Mechanics

by Marvin Chester

What does quantum mechanics tell us about the key model physical systems of nature? The author of this highly regarded text explores this question in a conceptual manner, fusing mathematical and philosophical elements to present physical imagery that closely parallels the mathematics.
Beginning with an overview that discusses the premise and design for the study, the text proceeds with an examination of the classical quantum bead on a its states and representations; its measurement spectra as operator eigenvalues; the harmonic bound bead in a symmetric force field; and the bead in a spherical shell. Other topics include spin, matrices, and the structure of quantum mechanics; the simplest atom; indistinguishable particles; and stationary-state perturbation theory.
Geared toward upper-level undergraduate students in physics, this refreshing and instructive text requires the following a freshman-year survey course in physics, a first course in classical Newtonian mechanics, and a grasp of mathematics that encompasses integral calculus, vector analysis, differential equations, complex numbers, and Fourier analysis.

Genres: Physics

336 pages, Paperback

First published June 9, 1987

Reviews

[WarpDrive · Rating 4 out of 5]

This is a quite nice, intermediate level book on Quantum Mechanics.

All major aspects of this discipline are treated (foundational postulates, wave function, Dirac notation, Schroedinger equation in several scenarios, discrete and continuous spectra, superposition of states, operators and matrix elements, Hamiltonian operators, commutation relationships, basis conversion, degenerate eigenvalues, angular momentum and spin, time-dependency, boson and fermions spin and symmetry of wave function etc.). This is a dense, rich book which provides lots of very useful information, to be read and kept for future reference.

As highlighted in its cover, this book is “geared towards upper-level undergraduate students in physics”; as such, it does require a good level of mathematical knowledge (differential/integral calculus, vector analysis, differential equations, complex numbers and Fourier analysis).

While most of the book is a pleasure to read, there are however some parts that I found unnecessarily complex and quite peculiar in approach. For example, I am not enthusiastic about how the author explains the angular momentum operator: I have always seen it explained according to the most general and fundamental definition (as the generator of rotations), or initially postulated as a natural extension from the classical definition. The author uses instead what I found an overly mathematical, indirect, unnecessarily obscure approach.

Moreover, a bit too much is left to the exercises (in my opinion, exercises should be devoted to providing examples, and to re-enforcing the message of the main text, not to substituting it), which detracts from the readability and fluidity of the main text. But for the most part these exercises are not impossibly complex, and hints and solutions are given for a good part of them.
I also found that, in some areas, you would need a separate book to flesh out the actual derivation of some formulas.

In some other areas, however, this book is really great: the chapter on indistinguishable particles, just as an example, which is very clear and particularly helpful.

Overall, a very good intermediate level book, rewarding and full of useful information; it just requires sufficient patience, devotion and attention.

[Sanjay · Rating 4 out of 5]

Its really a primer for the subject. It teaches you concept very beautifully and with simplicity and without creating any unnecessary fuss.There are no hardcore and rigorous derivations.

He either comes to the result intuitively or simply state the result without going into hardcore derivations. But the insights given in the book make up for the lack in derivations.

[Jens · Rating 5 out of 5]

Highly recommended textbook! I am a self-learner in physics and I got a lot out of this book, despite it being primarily used as a course book. My previous knowledge includes Susskind's Theoretical Minimum which is a good taster for this main dish, knowledge on general mathematics and classical physics is of course a prerequisite too (again, Susskind can help you out). I found Daniel Fleisch to be an excellent help too, specifically A Student's guide to Waves for the Fourier theory and a very enlightening section on the wave-function and Schrödinger equation.
Of course QM takes a lot of hard work to get through. I read the book twice and did exercises (not all, I will now return to do the rest of them) which took me about 3-4 hours every day for about 1.5-2 months (with some off days) but now feeling pretty confident in my understanding. I will probably attempt to do an online course on it if I can find one, to test my mettle so to speak.

The book does not talk about so-called Old quantum theory but jumps right into the wave-function of a particle on a closed loop. This means Fourier and Dirac delta-functions come in first rather than spin matrices, as Susskind approaches it. I like this book's approach better because it leads to a very smooth path to spin by translating position- and momentum-space into polar coordinates, rather than taking it for granted to explain the mathematical apparatus. It better shows the elegance of the theory. Of course I may be biased because I first experienced the matrix view and only then the wave-view, already having some understanding at that point.
The derivations are not rigorous which is, to me, a huge plus. I don't see much use in proving things that are established by experiment anyway, proofs and axioms are best left to the mathematicians and their masochist tendencies.
As one reviewer commented, derivations are often not fully given in the text but referred to the exercises, but aren't too difficult to do by pencil in the margins. Nevertheless I won't deny I had some tough goings in a few places. But that's only natural in this topic.

I would encourage everyone who is interested in the subject and is looking for more than superficial word-explanations in popular physics books. The theory really is so extremely beautiful and elegant as they say and only by seeing the mathematical machine churning can you appreciate that. To my mind, especially philosophers ought to be interested in quantum theory and take a deep look into its bowels because the implications for our picture of the universe are truly profound. With reading this I have now gained such a wonderful new realm of ideas and concepts to be amazed by that it very generously repays the hard work I put into it.