Quantum mechanics Definition and 994 Threads

What is the difference between a vector and a vector space? I get that a vector is an object with both magnitude and direction, but am confused by the term "vector space". Does a vector space simply refer to a collection of vectors? Thanks!

There is only one way to reduce the equations of special relativity (aka Lorentz Transformations) to the equations of Newtonian mechanics (aka Galilean Transformations). In light of the above, why are there multiple ways to reduce quantum-mechanical equations of motion into classical equations...

Homework Statement Rewrite the state |ψ⟩ = √(1/2)(|0> + |1>) in the new basis. |3⟩ = √(1/3)|0⟩ + √(2/3)|1⟩ |4⟩ = √(2/3)|0⟩ − √(1/3)|1⟩ You may assume that |0⟩ and |1⟩ are orthonormal. Homework Equations The Attempt at a Solution [/B] I have a similar example in my notes however there...

Hi what are the recommended quantum mechanics books for a high school leaver. Also what are the math skills I need to know(book suggestions would help). Please I need to understand QM. I'm just interested!

I'm interested in quantum mechanics but I am not sure where to begin. I have a a good understanding of classical mechanics, but I don't know where to start in quantum mechanics. I seem to dive into subjects that are too complicated for me to understand at the moment. Where is a good starting...

I am looking for a textbook for learning quantum mechanics. So, i have never had a course in quantum mechanics(currently in a class called modern physics where they introduce us to modern physics topics, but no qm classes) So, I was looking for book for self learning. I might take graduate...

Homework Statement "Show that the Hermite polynomials generated in the Taylor series expansion e(2ξt - t2) = ∑([FONT=Book Antiqua]Hn(ξ)/n!)tn (starting from n=0 to ∞) are the same as generated in 7.58*." 2. Homework Equations *7.58 is an equation in the book "Introductory...

I'm currently self-studying quantum mechanics and instead of starting a new thread every time I have a new question I figure I'd just make one thread dedicated to all of them. I'm going over the Photoelectric Effect. The way I understand it is when light is shone on a metallic surface, the...

Homework Statement Demonstrate that the expectation value of momentum (p) for the wave function: ψ(x)∝e^(-γx) when x>0, ψ(x)=0 when x<0. Hint: Pay special attention to the discontinuity at x=0.[/B] Homework Equations <p>=<ψ|p|ψ>=∫dxψ*(x)[-iħ∂/∂x]ψ(x) from -∞ to ∞. [/B]The Attempt at a...

Homework Statement A particle of mass m in the one-dimensional harmonic oscillator is in a state for which a measurement of the energy yields the values ##\hbar\omega/2## or ##3\hbar\omega/2## each with a probability of one-hald. The average value of the momentum ##\langle p_x\rangle## at...

Hello, I have a conceptual problem. How can both General Relativity and a theory of Quantum Gravity simultaneously exist? GR describes gravity as the curvature of spacetime, while QG is most likely a gauge theory. Furthermore, if gravity is indeed describedby particle interactions-what does...

Homework Statement Consider a particle in an energy eigenstate ##|n\rangle.## Calculate ##\langle x\rangle## and ##\langle p_x\rangle## for this state. Homework Equations ##x = \sqrt{\frac{\hbar}{2m\omega}}(a+a^{\dagger})## The Attempt at a Solution ##\langle x\rangle =...

Why do Complex Numbers arise in Quantum Mechanics' computations? What kind of physical significance do they carry? Someone told me to read this paper: W E Baylis, J Hushilt, and Jiansu Wei, Why i?, American Journal of Physics 60 (1992), no. 9, 788–797. But I found it difficult for me to...

I do not understand a work example in the book: ‘Quantum Mechanics DeMystified”. On page 212, part of Example 7-5: Given: Let { |a> |b> } be an orthonormal two-dimensional basis Let Operator A be given by: A = |a>< a |- i| a><b |+ i| b><a |- |b><b | Then: (The following part I do not...

THE “INTELLIGENCE” BEHIND QUANTUM PHYSICS If the nature of quantum mechanics is that an observer affects the end “collapsed” state of a particle, than what constitutes a state of observation. The the only thing I can come up with that seems to determine what constitutes a form of observation is...

I know that nuclear engineering requires some quantum mechanics but I want to know how much. Are there any textbooks that can fulfill the requirements for quantum mechanics in terms of nuclear engineering? I have heard of this book and I am a fan of old fashioned...

Hi, I've been self studying physics for a few years and I'm looking for some new books, specifically on Quantum Mechanics or Quantum Chemistry. It doesn't matter if they are PDF files or actual books, and price doesn't really matter. I've read Feynmans Lectures books and I'm looking for the next...

In many textbooks, the non-commutativity for the canonical pair is considered to lead to the major variaty from classical mechanism(CM) to quantum mechanism(QM), and change the Possion bracket into quantum commutator is a standard procedure called as canonical quantization. But in fact the...

I have just started reading about a classical electromagnetic treatment of light-matter interaction (beginning with dispersion relations, and then moving on to the standard phenomena - reflection, refraction, etc.). The discussion begins with a forewarning that light is not 'continuous' as the...

Homework Statement Normalize the wave function $$ \langle x|\psi\rangle = \left\{ \begin{array}{l l} Ne^{-kx} & \quad x>0\\ Ne^{kx} & \quad x<0 \end{array} \right..$$ Determine the probability that a measurement of the momentum p finds the momentum between ##p## and ##p + dp## for this wave...

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...

I have been looking online for books on introductory level quantum mechanics and General relativity that provide a mathematical introduction to these theories. Most of the books I have read until now provide a laymans introduction to these things. Since I'm only pursuing this as a hobby and...

Homework Statement Let ##|\psi\rangle \to |\psi'\rangle = \hat{T}(\delta x)|\psi\rangle## for infinitesimal ##\delta x##. Show that ##\langle x \rangle = \langle x \rangle + \delta x## and ##\langle p_x \rangle = \langle p_x\rangle.## Homework Equations ##\hat{T}(\delta x) =...

Hey I'm new to this forum and I'm 14 and I want to be a future Physicist (Probably Particle Physicist ) and I was wondering what books are good for starting out , just to let you know what kind of content I'm looking for I already know about General relativity , special relatativity , and the...

Hi, I know this is a basic question however, I am seeking absolute verification on these two points. 1) Quantum Mechanics is a set of Laws. 2) Laws only describe what we see. Theories give us the reason behind them.

Homework Statement Let ##\langle\psi| = \int^{\infty}_{-\infty}dx\langle\psi|x\rangle\langle x|.## How do I calculate ##\langle\psi|\psi\rangle?## Homework Equations ##\int^{\infty}_{-\infty}dxf(x)\delta(x-x_0)=f(x_0)## The Attempt at a Solution ##\langle\psi|\psi\rangle = \int\int...

According to laplace,universe is totally deterministic.(one can tell position of object future position of object if he knows current position and velocity)but Heisenbergs's tells us that there is always uncertainty in position of particle and velocity.but Heisenberg's uncertainty only applies...

Homework Statement The wave function of a certain particle is Ψ= A cos^2(x) for -π/2 < x < π/2. Find the value of A. Homework EquationsThe Attempt at a Solution My answer is coming out to be zero wheres as the correct answer is under root 8/3π ... Please help me out !

Hello! What are the requirements in physics and mathematics that somebody must have in order to start learning Quantum Mechanics by himself?

I have often heard that in quantum mechanics time has no direction. That the physics works the same going backwards in time than forwards. How does the wave function collapse of a particle follow this idea? If we could see time go backwards would we see particles turning back into waves? Is...

Homework Statement [/B] Just trying to find the spin 3/2 rotation matrix, I've found spin 1/2 and spin 1. This isn't a homework problem just studying some other spins. Homework Equations For spin 1/2: Rn(Φ) = cos(Φ/2)1ˆ − isin(Φ/2)σn For spin 1: Un(Φ) = e −iΦSn = 1ˆ − isin(Φ) · Sn − (1ˆ −...

Homework Statement Consider the Hamiltonian: $$\hat{H}=C*(\vec{B} \cdot \vec{S})$$ where $C$ is a constant and the magnetic field is given by $$\vec{B} = (0,B,0) $$ and the spin is $$\vec{S} = (\hat{S}_{x},\hat{S}_{y},\hat{S}_{z}),$$ with$$\hat{S}_{x}...

Homework Statement Particle of mass [tex[m[/tex] is confined on the ring of constant radius r_0. Solve Schroedinger equation for this problem. Homework EquationsThe Attempt at a Solution Problem is solved here http://www.physics.oregonstate.edu/~corinne/COURSES/ph426/notes3.pdf Why...

I'm learning about the Schrödinger equation in one of my uni courses, and we've recently gone past how to solve the time-independent version. That got me wondering if there is a space-independent version of the Schrödinger equation and what it could possibly be used for. I know I'm probably...

Hi, We know the convergence of a series but what does it mean to say that "an operator converges or diverges"?

Most probably, there was already a thread about this before, but I didn't find any with the search engine. Please, believe me, I tried a lot of words and found nothing like I'm going to ask now. I'm not a physicist...in fact, I'm a Political Sciences student with a great passion for Philosophy...

Hello! If we consider a single-particle system, I understand that the measurement of an observable on this system will collapse the wave function of the system onto an eigenstate of the (observable) operator. Therefore, we know the state of the system immediately after the measurement. But as...

Homework Statement How can I find the matrix representation of ##\mathbb{S}_+## and ##\mathbb{S}_-## in the ##|\pm y\rangle## or ##|\pm x\rangle## basis?Homework Equations ## \mathbb{\hat{S}}_+|s,m\rangle = \sqrt{s(s+1)-m(m+1)}\hbar|s,m+1\rangle ## The Attempt at a Solution The book almost...

Homework Statement When calculating expectation values for spin states I encountered ##\langle \hat{\mathbb{S}}_+\rangle = \langle+z|\hat{\mathbb{S}}_+|+z\rangle = \frac12\langle+z|\hat{\mathbb{S}}_++\hat{\mathbb{S}}_-|+z\rangle.## How do we compute...

Homework Statement Use the spin##-1## states ##|1,1\rangle, \ |1,0\rangle, \ |1, -1\rangle## as a basis to form the matrix representations of the angular momentum operators. Homework Equations ##\mathbb{\hat{S}}_+|s,m\rangle = \sqrt{s(s+1)-m(m+1)}\hbar|s,m+1\rangle##...

Homework Statement I am trying to find the possible measurement results if a measurement of a given observable ##Q=I-\left|u\right\rangle\left\langle u\right|## is made on a system described by the density operator ##\rho={1 \over 4}\left|u\right\rangle\left\langle u\right|+{3 \over...

Suppose we have a spin##-1## particle in a certain state ##|\phi\rangle## under the ##S_z## basis. How do you find the probabilities that a measurement of ##S_z## will result in the values of ##\hbar,0,## or ##-\hbar##? Also, what does it mean exactly when it says what is the probability that...

Homework Statement Show that for hydrogen the matrix element <2 0 0|z|2 1 0> = -3a0 where a0 is the Bohr Radius. On account of the non-zero value of this matrix element, when an electric field is applied to a hydrogen atom in its first excited state, the atom's energy is linear in the field...

Homework Statement Determine the eigenstates of ##\hat{\mathbb{S}}_x## for a spin##-1## particle in terms of the eigenstates ##|1,1\rangle, \ |1,0\rangle,## and ##|1,-1\rangle## of ##\hat{\mathbb{S}}_z.##Homework EquationsThe Attempt at a Solution Not sure exactly how to set this problem...