# What is Sakurai: Definition and 79 Discussions

Sakurai (桜井市, Sakurai-shi) is a city located in Nara Prefecture, Japan. As of March 31, 2017, the city has an estimated population of 58,386, and 24,629 households. The population density is 590 persons per km², and the total area is 98.92 km².

View More On Wikipedia.org
1. ### Quantum Modern Quantum Mechanics 3rd Ed: J. J. Sakurai & Jim Napolitano Review

Is Modern Quantum Mechanics, 3rd Edition, by J. J. Sakurai and Jim Napolitano a good book to learn quantum mechanics from?
2. ### Quantum Video lecture suggestion for Sakurai quantum mechanics Textbook

hello! I've been trying to read through Sakurai's Modern quantum mechanics textbook ( My goal is to finish the first 3 chapters and understand the Dirac formulation of QM specifically) but I find myself stumbling at many places. Are there any video lectures on the internet that follows this text...

4. ### Quantum Quantum Mechanics Textbooks: Alternatives to Sakurai

The assigned textbook for my quantum mechanics class is Sakurai, but I find it too concise and struggle to solve any of the problems. I feel like I understood very little so far because of it and am looking for some alternatives/supplements. Currently I'm torn between Townsend, Ballentine, and...
5. ### I Matrix Representation of an Operator (from Sakurai)

Look, I am sorry for not being able to post any LaTeX. But I am stuck at a place where I feel I should not be stuck. I can not figure out how to correctly do this. I can't seem to recreate the Pauli matrices with that form using the 3 2-dimensional bases representing x, y, and z spin up/down...
6. ### Quantum Physics Prereqs for Sakurai's Modern Quantum Mechanics

Hello, I've seen some ask about math prereqs for Sakurai's Modern Quantum Mechanics, but I was wondering about the physics prereqs as well. Should classical mechanics and electrodynamics be studied beyond first-year physics courses? Also, is statistical physics needed? What are the physics...
7. ### Two-level quantum system (from Sakurai)

Homework Statement Sakurai, problem 1.11 A two-state system is characterized by the Hamiltonian $$H = H_{11} | 1 \rangle \langle 1| + H_{22} | 2 \rangle \langle 2| + H_{12} \left[ | 1 \rangle \langle 2| + | 2 \rangle \langle 1| \right]$$ where ##H_{11}##, ##H_{22}##, and ##H_{12}## are real...
8. ### Quantum Modern QM by Sakurai and Napolitano

I have recently received an inspection copy of the 2nd edition of Modern Quantum Mechanics by Sakurai, now co-authored by Jim Napolitano. Here goes some free publicity: I love this book! It is like the old Sakurai, simply better. I know that many here at PF recommend Sakurai for advanced...
9. ### Quantum Thoughts on Sakurai's Quantum Mechanics textbook

I have taken a couple of graduate level courses in quantum mechanics and I have decided to read Sakurai's Modern Quantum Mechanics from cover to cover, partly because I liked his style and I have heard a lot of people talk highly of it. But I recently realized that the second edition of the same...
10. ### A Question while I study Modern Quantum physics by Sakurai

In the book of Modern Quantum physics by Sakurai I wonder how 1.6.26 can be 1.6.27.
11. ### Quantum Sakurai International Edition Missing Chapter

This is regarding Sakurai Napolitano's Modern Quantum Mechanics 2nd Edition (as opposed to the revised edition). It seems that the chapter 8 on the Relativistic Quantum Mechanics is missing from all Pearson International Editions (printed in Indian subcontinent or Malaysia/Thailand [Person New...
12. ### Answer to Sakurai 2.22 makes no sense

Homework Statement Consider a particle of mass m subject to a one-dimensional potential of the following form: (1/2)k*x^2 x>0 Infinity for 0<x Find <x^2> for the ground state Homework Equations <x^2>= <Psi|x^2|Psi> The Attempt at a Solution I know the answer is 3*h/(4*m*w) but to me...
13. ### Quantum "Modern Quantum Mechanics" by Sakurai for First Encounter

Dear friends, Can "Modern Quantum Mechanics" by Sakurai be used as a first introduction to the quantum mechanics, given that I have a professor who can guide my reading and supplementary books? I recently got an opportunity for a reading course in rigorous QM, and I thought Sakurai would be a...
14. ### Quantum Additional textbook to Sakurai and Ballentine

Hi. I already have Sakurai and Ballentine. I am looking for another textbook at a similar level. I am considering Gottfried & Yan , "Quantum Physics" by Bellac , "Quantum Mechanics" by Auletta. Any thoughts on these textbooks or any other suitable alternatives ? I do like textbooks that have...
15. ### Sakurai Modern Quantum Mechanics (Second Edition) Eq. 1.7.15

Homework Statement Reading Sakurai I cannot see how he gets to the end of 1.7.15 as below: Homework Equations ∫dx'|x'><x'-dx' |α> = ∫dx'|x'>{<x' |α>-Δx'∂/∂x'<x' |α>} The Attempt at a Solution I tried a Taylor expansion but cannot see how this is derived.
16. ### A Degenerate perturbation theory -- Sakurai

I'm reading section 5.2 "Time-Independent Perturbation Theory: The Degenerate Case" of the book "Modern Quantum Mechanics" by Sakurai and Napolitano and I have trouble with some parts of the calculations. At firsts he explains that there is a g-dimensional subspace(which he calls D) of...
17. ### Studying Learn QFT: From Sakurai to Group Theory & Beyond

Hello everyone, First of all, I am a third year undergraduate student. I have just finished studying (on my own) Sakurai' s "Modern Quantum Mechanics" (and I have done almost all exercises). I have taken courses in Complex Analysis (contour integration, residues etc) and in PDE (unfortunately...
18. ### Quantum Modern Quantum Mechanics Sakurai

What I'm going to need to learn from this book? I'm going to need read something before?
19. ### Spin 1/2 systemin Sakurai quantum mechanics

Homework Statement Homework Equations This is a passage from Modern Quantum Mechanics by Sakurai ( page 26~27) The Attempt at a Solution I wonder how i can get 1.4.8 , 1.4.9 equations . and what do they mean?
20. ### Sakurai Question regarding density matrix

Homework Statement Sakurai Modern Quantum Mechanics Revised Edition. Page 81. density matrix p = 3/4 [1 0; 0 0] + 1/4 [1/2 1/2; 1/2 1/2]. We leave it as an exercise to the reader the task of showing this ensemble can be decomposed in ways other than 3.4.24Homework Equations 3.4.24 w( sz +...
21. ### Math for Modern Quantum Mechanics J.J. Sakurai

Hi Guys, I am taking a quantum mechanics course next semester that follows Sakurai's book. I was wondering if there was some mathematics I should study over break in preparation for this course. I have taken so far: Calc 1-3 ODEs PDEs Linear Algebra An elementary course in group theory Ill...
22. ### Quantum Math requirement for J.J. Sakurai?

What math should a person know to THOROUGHLY understand everything in this textbook (J. J Sakurai. Modern Quantum Mechanics)? (For refrence) cal2 cal3 diffeq1(ode) diffeq2(pde) linealg vectorcalc realanal1 realanal2
23. ### Elementary quantum spin in Sakurai

Homework Statement I am currently working on a seemingly straightforward eigenvalue problem appearing as problem 1.8 in Sakurai's Modern QM. He asks us to find an eigenket \vert\vec S\cdot\hat n;+\rangle with \vec S\cdot\hat n\vert\vec S\cdot\hat n;+\rangle = \frac\hbar 2\vert\vec S\cdot\hat...
24. ### Self-Study Graduate Quantum Theory with Sakurai: Lecture Notes and Resources

Hello science buddies, This is my first post in this forum. Ok let me get to the point directly, currently I self-study graduate level quantum theory and the main book I'm using is Sakurai's. But I think for self studying it's better to also have a look at lecture notes, first because it's much...
25. ### Quantum Math requirements of QM by J. J. Sakurai?

What math should a person know to THOROUGHLY understand everything in this textbook(J. J Sakurai. Modern Quantum Mechanics)? (For refrence) cal2 cal3 diffeq1(ode) diffeq2(pde) linealg vectorcalc realanal1 realanal2
26. ### Possible Logical Flaw in Sakurai

So I'm trying to work my way through Sakurai's quantum in prep for grad school, and I'm so tied up by one of his steps in a theorem that I can't help but think the logic is flawed. It's theorem 1.1 on page 17 of the second edition. The theorem is as follows: The eigenvalues of a Hermitian...
27. ### Sakurai - Constructing 2x2 matrix from scalars?

Hello all, I am beginning a course in QM with Sakurai's 2nd Edition book on QM. In one of our problems, he defines a matrix as the sum of a scalar and a dot product... This seems like nonsense to me, but he uses the same notation in the next problem, so I am guessing this is some unorthodox...
28. ### Sakurai Degenerate Perturbation Theory: projection operators

Hi, So, I am working through section 5.2 of Sakurai's book which is "Time Independent Perturbation Theory: The Degenerate Case", and I see a few equations I'm having some trouble reconciling with probably because of notation. These are equations 5.2.3, 5.2.4, 5.2.5 and 5.2.7. First, we...
29. ### Didn't understand what Sakurai meant by this.

In Sakurai (Quantum Mechanics) (See attached). What is meant by "which is what we expect by substitution of ∇' "? Do they mean that I have to substitute it above and I should get equation (2.6.30)? Because I tried but couldn't simplify further. Thanks in advance.
30. ### What Is the Probability of Measuring Spin-up for Electron in State Alpha?

hello guys Suppose an electron is in the spin state alpha=(a,b). if s_y is measured, what is the probability of result h/2 ? s_y eigenvector for +h/2 is |y+>=1/sqrt(2) (1,i)) so the probabilty is (<y+|alpha>)^2 . but in the solution i attached , the solution is different ! I'm confused ...
31. ### Question about a Problem from Sakurai

Hello! I am studying the Sakurai book on Quantum mechanics and I am doing a problem. I have the solutions to the problems to help me understand the material better but I do not understand this solution. Homework Statement SEE "Sakurai Problem 1" in attachments K is the propagator...
32. ### Sakurai page 196: Orbital angular momentum as rotation generator

From "Modern Quantum Mechanics, revised edition" by J.J. Sakurai, page 196. Equation (3.6.4), 1-i \left( \frac{\delta \phi}{\hbar} \right) L_z = 1 - i \left( \frac{\delta \phi}{\hbar} \right) (x p_y - y p_x ) Making this act on an arbitrary position eigenket \mid x', y', z' \rangle...
33. ### Sakurai page 181: Time evolution of ensembles

From "Modern Quantum Mechanics, revised edition" by J. J. Sakurai, page 181. Equation (3.4.27), at some time t_0, the density operator is given by \rho(t_0) = \sum_i w_i \mid \alpha^{(i)} \rangle \langle \alpha^{(i)} \mid Equation (3.4.28), at a later time, the state ket changes from \mid...
34. ### Sakurai page 91: Simple Harmonic Oscillator, trouble understanding

From page 91 of "Modern Quantum Mechanics, revised edition", by J. J. Sakurai. Some operators used below are, a = \sqrt{\frac{m \omega}{2 \hbar}} \left(x + \frac{ip}{m \omega} \right)\\ a^{\dagger} = \sqrt{\frac{m \omega}{2 \hbar}} \left(x - \frac{ip}{m \omega} \right)\\ N = a^{\dagger}...
35. ### Sakurai page 54: Is this a Taylor expansion?

From page 54 of 'Modern Quantum Mechanics, revised edition" by J. J. Sakurai. Obtaining equation (1.7.15), \begin{eqnarray} \left(1- \frac{ip\Delta x'}{\hbar} \right) \mid \alpha \rangle & = & \int dx' \mathcal{T} ( \Delta x' ) \mid x' \rangle \langle x' \mid \alpha \rangle \\ & = & \int...
36. ### Modern Quantum Mechanics: J.J. Sakurai's eq. (1.7.31) Explained

From "Modern Quantum Mechanics, revised edition" by J.J. Sakurai, page 56. In equation (1.7.31) it is given, \begin{eqnarray} \delta(x' - x'') & = & | N |^2 \int dp' \exp \left[ \frac{ip'(x'-x'')}{\hbar} \right] \\ & = & 2 \pi \hbar | N |^2 \delta(x' - x'' ) \end{eqnarray} How does the...
37. ### J.J. Sakurai: Error of 2nd Order in d x' Eq (1.6.24)

From page 46 of "Modern Quantum Mechanics, revised edition", by J.J. Sakurai. In equation (1.6.24), \left[\mathbf{x}, \mathcal{T}(d\mathbf{x'}) \right] = d \mathbf{x'} \mid \mathbf{x'} + d \mathbf{x'} \rangle \approx d \mathbf{x'} \mid \mathbf{x'} \rangle It is written: "where the error...
38. ### Sakurai : Approximations in the construction of Quantum theory

From 'Modern Quantum Mechanics, revised edition' by J.J. Sakurai, In page 44 the translation (spacial displacement) operator \mathcal{T}(d \boldsymbol{x'}) is introduced. \mathcal{T}(d \boldsymbol{x'}) \mid \boldsymbol{x'} \rangle = \mid \boldsymbol{x'} + d \boldsymbol{x'} \rangle It is...
39. ### Sakurai - Modern Quantum Mechanics - page 34, equation (1.4.49)

Homework Statement From page 34 of 'Modern Quantum Mechanics' by J.J. Sakurai, The book considers 2 cases of sequential Sern-Gerlach like selective measurements. First case: There are 3 filters. The first (A) filter selects \mid a' \rangle and rejects all others, second (B) filter...
40. ### Sakurai page 27: What is this 'delta_1'?

In page 26 of 'Modern Quantum Mechanics (Revised edition)' by J.J. Sakurai, equation (1.4.9), they find the S_x + ket, \mid S_x;+ \rangle = \frac{1}{\sqrt{2}} \mid + \rangle + \frac{1}{\sqrt{2}} e^{i \delta_1} \mid - \rangle with \delta_1 real. What is this \delta_1? Furthermore, equation...
41. ### Quantum Modern Quantum Mechanics by J. J. Sakurai

Author: J. J. Sakurai (Author), Jim J. Napolitano (Author) Title: Modern Quantum Mechanics Amazon Link: https://www.amazon.com/dp/0805382917/?tag=pfamazon01-20 Prerequisities: Contents: Contents 1. Fundamental Concepts 1.1 The Stern-Gerlach Experiment 1.2 kets, Bras, and...
42. ### Sakurai proof Wigner-Eckart theorem

On page 240 in Sakurai's book "Modern Quantum Mechanics" (Revised edition) you can find a proof of the Wigner-Eckart theorem. I don't understand how you can deduce equation (3.10.36) from equation (3.10.35). I also don't understand why this proportionality factor is independent of m, q and m'...
43. ### Sakurai 1st edition vs. Sakurai 2nd edition?

Hi, I was wondering if anyone has had a chance to check out Sakurai/Napolitano's 2nd edition of Modern Quantum mechanics. Better or worse than the revised first? Thanks!
44. ### Dirac notation and conjugate transpose in Sakurai

In Sakurai's Modern Quantum Mechanics, he develops the Dirac notation of bras and kets. In one part, he states (page 17): <B|X|A> = (<A|X^|B>)* = <A|X^|B>* where X^ denotes the Hermitian adjoint (the conjugate transpose) of the operator X. My question is, since a bra is the conjugate...
45. ### Confusing step in Sakurai Chapter 1

Hi, At one point in Chapter 1 of Sakurai he is deriving the momentum operator in the position basis - I just don't see how he makes some of the mathematical leaps (at least leaps for me) between the following expressions \int dx' |x' + \Delta x'> < x' | \alpha > = \int dx' | x' > < x' -...
46. ### Which Version of Sakurai's Quantum Book Should I Get?

The required textbook for my grad level quantum course is Sakurai's quantum book, 2nd edition. However, there seem to be several versions of the 2nd edition text, ranging from $25 to$155. Is the newest version of the 2nd edition book significantly different/better from other versions that...
47. ### Sakurai: gravitational repulsion

Hi, I was reading Sakurai's "Invariance Principles and Elementary particles". In first chapter, second paragraph (page 3), there is a line "The analogous dimensionless constant that characterizes the gravitational repulsion between two protons is ...". Any body likes to comment on this, why...
48. ### Courses Sakurai as a first course in QM

I'm a junior undergraduate who has yet to take quantum mechanics, although I did have a brief introduction to basic wave mechanics (square well, harmonic oscillator, tunneling, the hydrogen atom, etc.) in "modern physics" course. I've also watched and taken notes from the Quantum Mechanics...
49. ### I am working out of Sakurai and he says the integral with respect to

I am working out of Sakurai and he says the integral with respect to p of exp(ip(x-x)/h-bar) is 2-Pi-h-bar times the dirac delta function of (x-x). (Sorry, I am not sure how to make actual integrals). I was wondering why this is true? For example, if x = x`, isn't the integral...
50. ### Time-reversal operator for fermions (Sakurai)

In Modern Quantum Mechanics (2nd ed.) by J.J. Sakurai, in section 4.4 on 'The Time-Reversal Discrete Symmetry' he derives the time-reversal operator, \Theta, for the spin-$\frac{1}{2}$ case as (pg.: 277, eq. (4.4.65)): \Theta = \eta e^{\frac{-i \pi S_{y}}{\hbar}}K = -i \eta \left(...