Quantum mechanics Definition and 994 Threads

May i know how do i eliminate C and D and how do i obtain the last two equations? Are there skipping of steps in between 4th to 5th equation? What are the intermediate steps that i should take to transit from 4th equation to the 5th equation?

In the context of non relativistic quantum mechanics, or better, if I consider the neutrino's mass to be zero, the phrase seems to me puzzling. What I know is that if I know the direction of motion, I know the spin projection onto that direction, say ##\hat{z}##-direction. But to not violate...

I can not solve this problem: However, I have a similar problem with proper solution: Can you please guide me to solve my question? I am not being able to relate Y R (from first question) and U (from second question), and solve the question at the top above...

is my solution correct?

This is a general property of eigenvectors of Hermitian operators. State functions are a particular class of vector, and it is easiest to work in the general formalism (I am hoping to show how ket notation makes qm easier, not just do standard bookwork at this level). Suppose O is a Hermitian...

A relativistic origin of QM is proposed in https://iopscience.iop.org/article/10.1088/1367-2630/ab76f7 It is proposed that lorentz transformation that include superluminal observers (whether those observers exist or not) explain the indeterministic behavior of QM. Not only that, it also would...

I need help .I did not A) E < V0 for T =? (passing coefficient ) B) E = V0 for T = ? C ) E > V0 for T =? A

In quantum mechanics in books authors discuss only cases ##E<V_0## and ##E>V_0##, where ##E## is energy of the particle and ##V_0## is height of the barrier. Why not ##E=V_0##? In that case for ##x<0## \psi_1(x)=Ae^{ikx}+Be^{-ikx} and for ##x\geq 0## \psi_2(x)=Cx+D and then from...

I was learning about Degenerate Perturbation Theory and I encountered the term 'Degenerate Subspace', I didn't really understand what it meant so I came here to ask - what does it mean? will it matter if i'll say 'Degenerate space' instead of 'Degenerate Subspace'? and subspace of what? (...

In R Shankar text on “principles of quantum mechanics’ discussing the adjoint operation, 1.3.8 shows that a|V> => <V|a*. Then 1.3.9 then states that <aV| = <V|a*. Is this a typo error?

How do "sinϕ - cosϕ sinϕ" become 0 ?

Summary:: Linear Quantum harmonic oscillator and expectation value of the potential energy (time dependent) Hello, I have attached a picture of the full question, but I am stuck on part b). I have found the expectation value of the <momentum> and the <total energy> However I am struggling with...

Homework Statement:: 1. Does the increase in kinetic energy in (for example) water that results from increasing its temperature result from electron excitation (i.e. increasing electron energy levels) or simply increasing their velocity or vibration amplitude/frequency? 2. If excitation is...

Fermilab's Don Lincoln describes Quantum Entanglement, and how it is different from classical statistics and hidden variables scenario.

Hello, I am struggling with what each piece of these equations are. I generally know the two rules that need to hold for an operator to be linear, but I am struggling with what each piece of each equation is/means. Lets look at one of the three operators in question. A(f(x))=(∂f/∂x)+3f(x) I...

https://www.nature.com/articles/d41586-020-00120-6

I'm self studying so I just want to ensure my answers are correct so I know I truly understand the material as it's easy to trick yourself in thinking you do! A particle of mass m is in a 1-D infinite potential well of width a given by the potential: V= 0 for 0##\leq## x ##\leq## a =...

According to Nobel laureate Frank Wilczek, the universe emerges from a Grid. This was proposed in his book "The Lightness of Being: Mass, Ether, and the Unification of Forces". He also likes the idea that the universe emerged from a state of "nothingness" (or rather, a quantum vacuum) where...

In 1935, Austrian physicist Erwin Schrödinger was looking at a concept called a "superposition." Superposition is when two waves meet and overlap and interact, which can lead to different results based on the circumstances. The concept can be seen in the regular-sized world as well, in...

In Quantum Mechanics, by Wigner's theorem, a symmetry can be represented either by a unitary linear or antiunitary antilinear operator on the Hilbert space of states ##\cal H##. If ##G## is then a Lie group of symmetries, for each ##T\in G## we have some ##U(T)## acting on the Hilbert space and...

I don't quite understand how he got the line below. By using discrete time approximation, we can get the second order time expression. But i don't see how by combining terms he is able to get such expression.

In the Many Worlds Interpretation's wikipedia article (https://en.wikipedia.org/wiki/Many-worlds_interpretation), it says, at the "Reception" part: "(...) On the other hand, the same derogatory qualification "many words" is often applied to MWI by its critics, who see it as a word game which...

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...

I'm considering a hydrogen atom placed in an infinite potential on one side of the nucleus, i.e. ##V(x) = +\infty## for ##x < 0##. I require the wavefunctions to be odd in order to satisfy the boundry condition at ##x=0##. By parity of the spherical harmonics only states with ##l## odd are...

Did Schrödinger believe that contradictory or inconsistent things could exist in reality?

This should be a trivial question. I am trying to compute the spherical tensor ##T_0^{(0)} = \frac{(U_1 V_{-1} + U_{-1} V_1 - U_0 V_0)}{3}## using the general formula (Sakurai 3.11.27), but what I get is: $$ T_0^{(0)} = \sum_{q_1=-1}^1 \sum_{q_2=-1}^1 \langle 1,1;q_1,q_2|1,1;0,q\rangle...

I have insertet the equations for H and P in the relation for the commutator which gives $$[H,P] = [\sum_{n=1}^N \frac{p_n^2}{2m_n} +\frac{1}{2}\sum_{n,n'}^N V(|x_n-x_n'|),\sum_{n=1}^N p_n] \\ = [\sum_{n=1}^N \frac{p_n^2}{2m_n},\sum_{n=1}^N p_n]+\frac{1}{2}[\sum_{n,n'}^N...

Hi everyone! This is the first time I'm posting on any forum and I'm still rather unsure of how to format so I'm sorry if it seems wonky. I'll try my best to keep the important stuff consistent! I am working on infinite square well problems, and in the example problem: V(x) = 0 if: 0 ≤ x ≤ a...

I have tried doing the obvious thing and multiplied the vectors and matrices, but I don't see a way to rearrange my result to resemble the initial state again: ##(\mathcal{D_{1y}(\alpha)} \otimes \mathcal{D_{2y}(\alpha)} )|\text{singlet}\rangle = \frac{1}{\sqrt{2}}\left[ \begin{pmatrix}...

Suppose I have a positive spin-##1/2## eigenstate pointing in the ##z##-direction. If I apply a rotation operator by an angle ##\theta## around the ##z##-axis the state should of course not change. However, if I write it out explicitly, I find something different: $$R_z(\theta)|\uparrow\rangle =...

I'd really appreciate it if someone could tell me where to obtain the solutions manual for Bransden and Joachin QM as I've been having a go at the problems.

Firstly, since there is no condition for the z axis in the definition of the potential can I assume that V(x,y,z) = .5mw^2z^2 when 0<x<a, 0<y<a AND -inf<z<inf? If so then drawing the potential I can see that the particle is trapped within a box with infinite height (if z is the...

Is the last inequality correct? Should it not be ##|A|^2 \cdot 2(1+\cos{(ka)})##? How is the time calculated here? Given ##\Delta v > 10^{-34}##... How come ##mv \Delta v = \Delta (\frac{mv^2}{2})##? Where does the ##(1/2)## come from?

EQ 1: Ψ(x,0)= Ae-x2/a2 A. Find Ψ(x,0) So I normalized Ψ(x,0) by squaring the function, set it equal to 1 and getting an A I. A=(2/π)¼ (1/√a) B. To find Ψ(x,t) EQ:2 Ψ(x,t)= 1/(√2π) ∫ ∅(k) ei(kx-ωt)dk --------->when ω=(ħk2)/2m and integral from -∞ to +∞ EQ 3: ∅(k)= 1/(√2π) ∫ Ψ(x,0)...

I started reading the book and I love it. In my opinion, even if you do not agree with the author's interpretation of quantum mechanics, it is a great read. Has anybody here tried reading it? The World According to Quantum Mechanics 2nd Edition by Ulrich MohrhoffHere are some abstracts.

I get so many different answers to this question so maybe here someone can pin this down. When I get up in the morning and I turn on my TV, I have over 3,000 channels so is there a universe with a version of me going to each channel? If not, how do I go to one channel over the other? Can my...

As a Computer Programmer, it's hard to wrap my head around Quantum Entanglement and non locality being explained in the context of Classical Physics. In other words, if the universe at it's core is physical where does Quantum Entanglement fit within a physical picture of reality? There's been...

In quantum mechanics, the Eigenfunction resulting from the Hamiltonian of a free particle in 1D system is $$ \phi = \frac{e^{ikx} }{\sqrt{2\pi} } $$ We know that a function $$ f(x) $$ belongs to Hilbert space if it satisfies $$ \int_{-\infty}^{+\infty} |f(x)|^2 dx < \infty $$ But since the...

Why can't there be a Universal Interpretation of Quantum Mechanics? If you unite Copenhagen and Many Worlds than all other interpretations will fall under the umbrella of a Universal Interpretation of Quantum Mechanics. The main problem with interpretations seems to be the role of the observer...

According to Everett-interpretation or many world interpretation of quantum mechanics, each decision an observer makes, the world splits into two parallel universes, let’s say an observer in some point in Spacetime is tests the Schrödinger’s cat experiment, in one branch of the universe the cat...

Summary: Could different outcomes have different physics in Wigner's friend? Physicist Eugene Wigner said that consciousness was fundamental for physics and that laws of physics existed because of it. He said that "consciousness can change the usual laws of physics" He also proposed the...

I can show that ##\frac{d}{dt} \langle \psi (t) \vert X^2 \vert \psi (t) \rangle = \frac{1}{m} \langle \psi (t) \vert PX+XP \vert \psi (t) \rangle##. Taking another derivative with respect to time of this, I get ##\frac{d^2}{dt^2} \langle \psi (t) \vert X^2 \vert \psi (t) \rangle = \frac{i}{m...

Hi everyone, was just wondering what people think is a good undergraduate QM book is as opposed to Griffiths. I've read through it, and I have looked and many people say it is good for people who've never been exposed to QM before, but when it comes to solving problems I struggle a lot, and...

Okay i was reading abrikosov's book and he said since in QM spin only changes by integer values boson excitiation happens one at a time and fermion ALWAYS appears or disappears in pairs. but isn't change from a spin up to spin down 1/2 to -1/2? or i had the wrong convention which |1/2| shouldve...

I calculated the complex conjugate of both the given wavefunctions. For ψ1: ∫re^((-2)mod(r)x)dx=1 with upper limit ∞ & lower limit -∞. I replaced the upper and lower limit after breaking down the function inside integration as follows- r*∫e^(2rx)dx from -1/r to 0 and r*e∫e^(-2rx)dx from 0 to...

So I am trying to understand and solve the problem mentioned in the title.I found a solution online: https://physics.bgu.ac.il/COURSES/QuantumMechCohen/ExercisesPool/EXERCISES/ex_9011_sol_Y09.pdf The problem is, I can't understand this step : I relly can't find out how the two expontential...

Summary: What did Omnès mean with this? I found an old article by Roland Omnès which analyzes the EPR paradox and offers a solution to it (https://www.sciencedirect.com/science/article/abs/pii/0375960189900182). At some point, the article says: "Some macroscopic systems do not satisfy the...

Suppose the unitary operator ##e^{-\frac{i}{\hbar}\hat{H}t}## acts on ##|\psi (0) \rangle##, does it make sense for one to think of the time-evolved state as some sort of time-keeping device? If not, why? If so, is such a notion useful? Thanks in advance!

As far as I know we can express the position and momentum operators in terms of ladder operators in the following way $${\begin{aligned}{ {x}}&={\sqrt {{\frac {\hbar }{2}}{\frac {1}{m\omega }}}}(a^{\dagger }+a)\\{{p}}&=i{\sqrt {{\frac {\hbar }{2}}m\omega }}(a^{\dagger }-a)~.\end{aligned}}.$$...

It's easy to show that ##[\Delta A, \Delta B] = [A,B]##. I'm specifically having issues with evaluating the bra-ket on the RHS of the uncertainty relation: ##\langle \alpha |[A,B]|\alpha\rangle = \langle \alpha |\Delta A \Delta B - \Delta B \Delta A|\alpha\rangle## The answer is supposed to be...