Quantum mechanics Definition and 994 Threads

According to one of the postulates of quantum mechanics, every measured observable q is an eigenvalue of a corresponding linear Hermitian operator Q. Which means, that q must satisfy the equation Qψ = qψ. But according to Griffiths chapter 3, this equation can only be followed from σQ = 0. It...

If one has two single-particle Hilbert spaces ##\mathcal{H}_{1}## and ##\mathcal{H}_{2}##, such that their tensor product ##\mathcal{H}_{1}\otimes\mathcal{H}_{2}## yields a two-particle Hilbert space in which the state vectors are defined as $$\lvert\psi ,\phi\rangle...

From my humble (physicist) mathematics training, I have a vague notion of what a Hilbert space actually is mathematically, i.e. an inner product space that is complete, with completeness in this sense heuristically meaning that all possible sequences of elements within this space have a...

I'm trying to prove the following relation $$\langle\psi\lvert \hat{A}^{\dagger}\rvert\phi\rangle =\langle\phi\lvert \hat{A}\rvert\psi\rangle^{\ast}$$ where ##\lvert\phi\rangle## and ##\lvert\phi\rangle## are state vectors and ##\hat{A}^{\dagger}## is the adjoint of some operator ##\hat{A}##...

Homework Statement I want to find the matrix representation of the ##\hat{S}_x,\hat{S}_y,\hat{S}_z## and ##\hat{S}^2## operators in the ##S_x## basis (is it more correct to say the ##x## basis, ##S_x## basis or the ##\hat{S}_x## basis?). Homework Equations...

Hello! I want to learn about the mathematics of General Relativity, about Topology and Differential Geometry in general. I am looking for a book that has applications in physics. But, most importantly, i want a book that offers geometrical intuition(graphs and illustrations are a huge plus) but...

I get that a if we have complete information of the state of the system (i.e. all the possible knowledge we could have about it: the values its observables can take and their corresponding probabilities), then it is a pure state and can be represented by a vector (ket), ##\lvert\psi\rangle## in...

Homework Statement Virtually all quantum mechanical calculations involving the harmonic oscillator can be done in terms of the creation and destruction operators and by satisfying the commutation relation \left[a,a^{\dagger}\right] = 1 (A) Compute the similarity transformation...

Introduction If Quantum Mechanics is more fundamental than General Relativity as most Physicists believe, and Quantum Mechanics is described using Hilbert Spaces wouldn't finding a compatible version of General Relativity that operates within the confines of a Hilbert Space be of utmost...

Currently I'm in the last year of the Physics course and I've been thinking about working in a project of undergraduate research, specifically in Statistical Physics. Two years ago I've already done a project like that in Fluid Mechanics combined with Gauge Theories and in that project I've...

In case of tunnel effect in quantum mechanics we often consider time independent Schroedinger equation with potential ##0##, when ##x<0## then some ##V_0## when ##0\leq x\leq a## and ##0## when ##x>a## so potential barrier problem. And energy of particle that we send to barrier is ##E<V_0##. In...

Just watched the documentary 'Stephen Hawking Grand Design: Did God Create The Universe'. S.H. stated that the big bang was similar to subatomic particles that appear, disappear and reappear somewhere else following the laws of quantum mechanics. If that were so, wouldn't it also be possible for...

Hello! I want to prove that the probability current is a continuous entity at the boundaries of the square for the situation of 0< E< Vo in the problem where V is zero except a finite region in space where it is +Vo and we consider an incoming particle from the left(for example). I thought that...

Can anyone suggest me a book on quantum electrodynamics for beginners? Thanks in advance

A. Neumaier submitted a new PF Insights post Misconceptions about Virtual Particles Continue reading the Original PF Insights Post.

In my lecture notes, it says that ##\left\langle l \right| A_{nm} \left| \psi \right\rangle = \sum_{n,m} A_{nm} \left\langle m \right| \left|\psi \right\rangle \left\langle l \right| \left| n \right\rangle## ##=\sum_{n,m} A_{nm}\left\langle m \right| \left| \psi \right\rangle \delta_{ln}## ##=...

H=p^2/2m+c What's c? It's of course a shift in energy, but can be thought also as a smoother and smoother real-space local potential that becomes a constant all over the space. On the other hand, why couldn't one think about it as a constant potential in reciprocal space? It's a shift in energy...

The problem asks for the diagonalization of (a(p^2)+b(x^2))^n, where x and p are position and momentum operators with the commutation relation [x,p]=ihbar. a and b are real on-zero numbers and n is a positive non-zero integer.I know that it is not a good way to use the matrix diagonalization...

jfizzix submitted a new PF Insights post Steering: How the EPR-Paradox Fits Between Entanglement and Nonlocality Continue reading the Original PF Insights Post.

If we were to assume that the electron moves around the proton with radius a, the Schrodinger equation becomes: ##\frac{1}{a^2}\frac{d^2\psi}{d\phi^2} + \frac{2m}{\hbar^2}|E|\psi = 0## The question in my textbook asks me to solve the above equation to obtain values of energy and angular...

Homework Statement Consider a spin system with noninteracting spin 1/2 particles. The magnetic moment of the system is written as: μ = (ħq/2mc)σ Where σ = (σx, σy, σz) is the Pauli spin operator of the particle. A magnetic field of strength Bz is applied along the z direction and a second...

is entropy problem easiest than quantum mechanics problem which one is more complicated to understand and to solve ?

I want to start learning quantum mechanics but i have no idea where to start . I want to know which other fileds and physics branches i have to study before quantum mechanics and if i want to go more deeply for this (like taking a graduate course ) what should i study before this in physics math...

Hello, This was part of my midterm exam that i couldn't solve. Any help is extremely appreciated. Problem: The K.E. of a rotating top is given as L^2/2I where L is its angular momentum and I is its moment of inertia. Consider a charged top placed at a constant magnetic field. Assume that the...

I heard of it several times in colloquiums. But I still cannot grasp the meaning. What is the control parameter in this phase transition?

I recently bought this book: https://www.amazon.com/dp/1107050405/?tag=pfamazon01-20 In the preface it says that I'm assumed to have already learned quantum mechanics (including angular momentum and Dirac equation) and nuclear physics at an introductory level. What does that mean? Do they mean...

Steven Weinberg has made what he calls a "modest proposal": http://arxiv.org/abs/1405.3483 Quantum Mechanics Without State Vectors Steven Weinberg (Submitted on 14 May 2014) It is proposed to give up the description of physical states in terms of ensembles of state vectors with various...

I don't know where I'm going wrong with this problem - I was so sure I had it right but the online grader tells me otherwise :oldfrown: Homework Statement An electron in a one-dimensional box has ground-state energy 2.60 eV. What is the wavelength of the photon absorbed when the electron...

For example, general relativity relates the behavior of gravity the the deformation of spadetime. But does quantum mechanics explain why particles behave the way they do? Or does it only explain how processes such as entanglement work not why they occur.

Hello all, as far as I can see this question is not posted already, my apologies if it is and please provide a link. But I'm watching this video on youtube: And at 22:38 there's an expression given for the uncertainty of an arbitrary operator Q, however I'm concerned the expression is incorrect...

Hello! It is sometimes useful to find the average energy of a certain number N of particles contained in a box of volume V. In order to find this quantity, the total energy is required and then divided by N. The result is E_{average} = \displaystyle \frac{1}{N} \sum_{n = 1}^{N} \left| a_n...

Hi, why there is only odd eigenfunctions for a 1/2 harmonic oscillator where V(x) does not equal infinity in the +ve x direction but for x<0 V(x) = infinity. I understand that the "ground state" wave function would be 0 as when x is 0 V(x) is infinity and therefore the wavefunction is 0, and...

Homework Statement a) Determine the ratio (Em/En) between two energy states of a particle in a one dimensional box of length l. b) Show that this is consistent with the non-relativistic low-energy limit. The attempt at a solution I have figured out a) using the de broglie wave-particle duality...

Homework Statement I have a particle which is initially in a bound state for a given voltage in the form of a delta function at the origin, V = -αδ(x) initial state is ψα = (√αm)/h2*exp(-m*α*|x|/(h2) At t=0, voltage is changed to V = -βδ(x) both α and β are greater than zero. Right now I'm...

Specifically, i do not know hot to express the potential in momentum space. If someone would provide me with a link of source that has the proof in it, it would be appreciated.

Not quite. But it necessarily has to be described by a different quantum model than unitary dynamics if it is an open system and the rest of the universe is not explicitly modeled. For convenience, physicists often want to describe a small quantum system in terms of only its Hilbert space, when...

In Griffith's "Introduction to Quantum Mechanics, second edition" he states: For the delta-function potential, when considering the scattered states (with E > 0), we have the general solutions for the time-independent Schrodinger equation: $$\psi(x) = Ae^{ikx} + Be^{-ikx}~~~~\text{for }x<0$$ and...

Homework Statement 5) A free particle moving in one dimension is in the state Ψ(x) = ∫ isin(ak)e(−(ak)2/2)e(ikx) dk a) What values of momentum will not be found? b) If the momentum of the particle in this state is measured, in which momentum state is the particle most likely to be found? c)...

I'll answer this in this thread, later today.

Hi Do Quantum Mechanics negates the reality of matter and proves un-reality of matter ?

Almost phenomena at macro level are classical phenomena,why physics needs QM very much?Is it rational need or practical need?

Quantum particles are not localized before they are observed, as shown with the Young double slit experiments and those with entangled particles. On the other side, vacuum is filled with virtual particles. Are the non-localized particles responsible for the virtual particles? or only for a part...

aleazk submitted a new PF Insights post Tools to Enrich our Quantum Mechanics Interpretations Discourse Continue reading the Original PF Insights Post.

Hello. I want to share a thought experiment that could tell Quantum Mechanics apart from Pilot-Wave interpretation. It goes like this: Quantum Mechanics vs. Pilot-Wave: Quantum Mechanics: Waves collapse to particles. Waves disappear when particles are detected. Pilot-Wave: Waves are real but...

So this is something that troubled me a bit- in Shankar's PQM, there's an exercise that asks you to find the position expectation value for the harmonic oscillator in a state \psi such that \psi=\frac{1}{\sqrt{2}}(|0\rangle+|1\rangle) Where |n\rangle is the n^{th} energy eigenstate of...

This question is a continuation/topic-extrapolation of: https://www.physicsforums.com/threads/flux-in-magnetic-core-according-to-special-relativity.856482/#post-5374651 My question is 'how is the electromagnetic field different from some sort of mere electric-charge field?' The issue I have...

Hi there! Can you please introduce me some books on advanced quantum mechanics which has solutions for its exercises. Of course, I know Shankar and Sakuraii, but, I mean something more advanced which covers these topics: (Scattering, Dirac Fields, Group Representations, Relativistic Quantum...

Hi All, Was there any use of the concept of amplitudes of probability before their use in quantum mechanics? In connection to this question, who invented or was the first to use this resource? Best wishes, DaTario

Homework Statement Given the following k-space representation of the wave function: Ψ(k,t) = Ψ(k)e-iħk2t/2m use the wave number representation to show the following: <x>t=<x>0 + <p>0t/m <p>t=<p>0 Homework Equations <x>=∫Ψ*(x,t)xΨ(x,t)dx <p>=∫Ψ*(x,t)(-iħ ∂/∂x)Ψ(x,t)dx The Attempt at a...