Quantum mechanics Definition and 994 Threads

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...

Hey guys, I want to build a strong and straight plan for my next years of studying and once finish I am able to do something on my own and come up with crazy ideas and actually test them, build some awesome algorithms, all that cool stuff, but I'm kinda stumble so it would be nice if someone...

Hello, I am curious if I have this correct and if it has a name. A thin walled cylinder is spinning on its axis along its length in a closed system. It begins to draw itself in converting its invariant mass to kinetic energy. In polar coordinates ##E=\gamma_\theta m c^2, L=\gamma_\theta m...

Summary: Does Richard Feynman's multiple histories ignore alternative histories? Did Richard Feynman's multiple histories (https://en.wikipedia.org/wiki/Multiple_histories) ignore the existence of other alternarive histories or paths? I ask this referring to this comment from this page...

The wave function described seems impossible. Wave functions have to be differentiable at all points, right? Otherwise they don't represent a physically realizable state. The wave function in the example isn't differentiable at x=A, the maximum point. Also, for problem (c), I know it's visually...

This question is inspired by a comment that @thephystudent made where he said that "The dephasing between the Bragg pulses is not unitary, I believe it can be explicitly written in Lindblad form and generates heat. I believe this Point of view is the same as (among others) the papers of...

David Deutsch, a theoretical physicist, talks about David Bohm in his book "the Fabric of Reality": "[w]orking out what Bohm’s invisible wave will do requires the same computations as working out what trillions of shadow photons will do. Some parts of the wave describe us, the observers...

Does quantum mechanics follow causality, phase transition, critical point, symmetry, asymmetry, order, disorder, continuation, discontinuation, limitation, without limitation, convergence, divergence, similarity, hierarchical structure, singularity, plurality?

Summary: please help me understand the following questions from Physics GRE test Thank you very much! To be honest i really hate this formalism. Memorizing such things is pain. but like everything it is what it is

Summary: Could MWI (Many Worlds Interpretation) create universes with fundamentally different physical laws? Physicist John Wheeler proposed along with Hugh Everett and Bryce DeWitt the 'Many Worlds' Interpretation of Quantum Mechanics (although he expressed some doubts about its validity) I...

I read in a book the following assertion. In a double slit experiment photons are passed through the slits and detected at the end plate. Each of the two slits has a quarter wave plate which alters the polarization of the photons that pass through it in a way different than the other QWP. Thus a...

According to general relativity, gravity is simply the side-effect of bending the geometry of space-time. As a thought experiment imagine a 3D image being projected from a 2D hologram - the distance between the actual 2D pixels in the 2D plane always remains constant, yet depending on the shape...

I'm getting confused by the perturbation theory aspect of problem 2.2 in this book. We have to show that the energy eigenvalues are given by $$E_n = \left(n + \frac{1}{2}\right) \hbar \omega + \frac{3\lambda}{4} \left(\frac{\hbar}{m\omega}\right)^2 (2n^2 + 2n + 1)$$ For the Hamiltonian...

In another forum, some people argue that time and space are discrete, due to Planck time and Planck length. However, I disagree with this idea. I think, the Planck time and Planck length are just some scales that we can measure, but they do not forbid continuous time and space shorter than...

Hello, I'm considering taking the graduate level quantum mechanics course offered at my university (based on Sakurai/Shankar). I am currently reading Sakurai's QM, and mostly understand the topics (I'm currently reading the theory of angular momentum). There have been some steps where I still...

How valid is the statement "It means physics is ultimately concerned with descriptions of the real world" in the realm of QM? Heretic question, what is "real" besides the outcome of the measurement?

The momentum operator for one spation dimension is -iħd/dx (which isn't a vector operator) but for 3 spatial dimensions is -iħ∇ which is a vector operator. So is it a vector or a scalar operator ?

Could one come to think that time is irrelevant in quantum mechanics? we know that the QM equations are written with the time variable, (schrodinger equation). Yet everything suggests that time is irrelevant, as the search for loop quantum gravity seems to indicate

Hello, I remembered once hearing of a must-have quantum mechanics book by Paul Dirac. I don't remember if it was his Principles of QM or Lectures on QM. Based on the table of contents, I believe it was the Principles of QM book; however, looking at both I was thinking about getting his Lectures...

A lecturer today told the class that relativistic QM for single particles is flawed by showing us that for a state centered at the origin, it was possible that ##Pr(\vec{x}>ct)>0##. He said that this was down to the fact that we should be considering multi-particle states in relativistic...

Why aren't you guys discussing this? http://de.arxiv.org/abs/1405.1548 The paper is 259 pages. And it will take me a year to read it. The Cellular Automaton Interpretation of Quantum Mechanics doesn't use any wave function. Just please tell me. How does it explain for example the double slit...

i want to know what is the most suitable quantum mechanics that will enables me after studying it to answer these specific questions ? i mean based on the hardness of these questions ( what book would you suggest to study these subjects ) . and by the way what is the level of these QM questions...

I've seen some articles that relate them (like this one: https://arxiv.org/pdf/1407.3118.pdf) "In this paper we will analyze the third quantization of gravity in path integral formalism. We will use the time-dependent version of WheelerDeWitt equation to analyze the multiverse in this...

Hi, I have a question, why when we study the Delta-Function Potencial we can treat with ##E < V##, since the following relation says ##\frac{d^2 \psi}{dx^2} = \frac{2m}{\hbar^2} (V - E) \psi## And do not allow it? or it is just ##E <...

In the double-slit experiment when a detector was placed before the two slits, a 2 strip pattern was produced after the two slits. When there was no detector placed before the two slits, a different pattern was produced after the two slits. Why does the presence of a detector before the two...

A particle has a 33% chance of being in either position 1, position 2, or position 3. After I observe it, it is in position 1, and not in position 2 or 3. Questions: How do we know it was not already in that position prior to us observing it? Does observation cause position, or is position...

Which of these premises is impossible or incorrect according to our current understanding of quantum entanglement? Given 2 entangled particles, p1 and p2: Observing paired particle p1 induces a change in spin on paired particle p2. There a way of detecting a change in spin on particle p2...

See Peter Shor's comments here and here and Urs Schreiber's comments here.

I think the effective action should make sense also in Quantum Mechanics, not only in QFT. But I have never seen described in a QM book as such. Could there be a QM book that uses effective actions? Or maybe in QM effective actions are called another name? I think effective actions in QM could...

I'd like to point to the book The Philosophy of Quantum Mechanics by C. Friebe et al., Springer 2018. It contains many topics usually underrepresented in foundational discussions of quantum physics, in chapters on many-particle systems and quantum field theory. It also has in its last chapter a...

Hello, I have a little problem understanding the quantum mechanics of a hydrogen atom. Im troubled with the following question: before i measure the state of a (simplified: without fine-, hyperfinestructure) hydrogen atom, which is the right probability density of finding the electron? is it...