Quantum mechanics Definition and 994 Threads

Hello Everyone, I am an undergraduate physics student who planned to study quantum mechanics. I have been reading the introductory book by Griffiths, however I found that his book seldom uses Dirac Notation and there is little about mathematical formalism on quantum mechanics. Therefore I would...

Hello, In my free time, I've been learning about an eclectic range of topics (ie. French History, Kinetic Theory etc.). Most recently I've been focused on Quantum Mechanics, which happens to be most complex topic I've ever looked at. Typically I write up summaries after reading from various...

What's the difference between relativistic quantum mechanics and quantum field theory? In principle, my guess is that to do the former, one needs to express the Hamiltonian in a relativistic, Lorentz invariant, form, because it seems to be the only frame-related term in the wave equation. (Is...

Homework Statement A particle of mass m and spin s, it's subject at next central potential: ## \begin{equation*} V(\mathbf{r})= \begin{cases} 0\text{ r<a}\\ V_0\text{ a<r<b}\\ 0\text{ r>b} \end{cases} \end{equation*} ## Find the constants of motion of the system and the set of...

In special relativity, we know, (proper time)^{2} = - (proper distance)^{2}. But, in Causal Dynamical Triangulations (CDT), they introduce an asymmetry parameter \alpha as, (proper time)^{2} = - \alpha (proper distance)^{2} [Q. 1] Can you please explain me about, why we need to introduce \alpha...

Homework Statement Referencing image attached. I'm not sure how the example arrived at ψ ⇒ 0 at x<0 and >L as K ⇒ ∞ in the limiting case of an infinite potential well. Homework EquationsThe Attempt at a Solution I tried simply applying limits to the wavefuction but in the case x<0, the...

Hi there - just a quick question about Fourier transforms: When learning about quantum mechanics, I found that the Fourier transform and inverse Fourier transform were both defined with constants of ##{ \left( 2\pi \right) }^{ -d/2 }## in front of the integral. This is useful, as...

Homework Statement I am currently reading a textbook on solving the Schrödinger equation for the harmonic oscillator using the series method; $$-\frac{\hbar^{2}}{2m}\frac{\mathrm{d}^2 \psi }{\mathrm{d} x^2}+\frac{1}{2}m\omega ^{2}x^2\psi =E\psi $$ It starts by using these two dimensionless...

I know that if the intensity of a light beam with of a certain frequency varies it means the number of photons the light beam is composed of varies and not the individual photons energy. That would mean the E and B field amplitudes vary. This would mean that that the amplitudes of the E and B...

So, I am a newbie in quantum mechanics, took modern physics last fall for my physics minor. I know that Schrodinger based his equation based on the equation K + V = E, by using non-relativistic kinematic energy (P2/2m + V = E) p becoming the operator p= -iħ∇ for the wave equation eigenfunction...

1. Amazon link: https://www.amazon.com/dp/0131118927/?tag=pfamazon01-20 ISBN: 978-0131118928 This is the book that my class syllabus suggests based off ISBN number, however it is $119.00 to buy off Amazon. 2. Amazon Link: https://www.amazon.com/dp/1107179866/?tag=pfamazon01-20 ISBN...

Hi, does treating neutrons as waves make any difference when it comes to micro cross sections ? , does quantum mechanics help more than classical mechanics in nuclear reactor physics ? Noticing that I am a nuclear engineering student

Homework Statement I have the criteria: ## <p'| L_{n} |p>=0 ##,for all ##n \in Z ## ##L## some operator and ## |p> ##, ## |p'> ##some different physical states I want to show that given ## L^{+}=L_{-n} ## this criteria reduces to only needing to show that: ##L_n |p>=0 ## for ##n>0 ##...

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...

Hi, people I wondered if as prerequisites for QM, the Kreyszig (for func. analysis) and Hassani's book they be suffices .. Thank you in advance !

If we consider a measurement of a two level quantum system made by using a probe system followed then by a von Neumann measurement on the probe, how could we determine the unitary operator that must be applied to this system (and probe) to accomplish the given measurement operators.

Hello, Let's suppose we have a two dimensional lattice which is periodic along certain direction, say x-direction, allowing us to define a quasi momentum k_x. The lattice is not periodic along the y-direction (perpendicular to x-direction). Therefore, we are able to obtain the band structure...

Physicists try to unite Quantum Mechanics and General Relativity. QM deals with three forces in nature (i.e., strong, weak , electromagnetism), while GR deals with geometry of space. How can one unite 3 forces and geometry? If one thinks of gravity as a force (not geometry), would one have a...

This may seem like a stupid question, but i can't get my head around this so please bear with me. I just looked at the derivation of Dirac equation and my question is: do the solutions for a free particle obey special relativity? because if yes why? I mean I thought using E2=(mc2)2+(pc)2 would...

In discussing stuff in another thread I used the standard Dirac notion expanding a state in position eigenvectors namely |u> = ∫f(x) |x>. By definition f(x) is the wave-function. I omitted the dx which is my bad but the following question was posed which I think deserved a complete answer. It...

I read paper https://arxiv.org/ftp/arxiv/papers/1011/1011.3719.pdf . I do not understand figure 2. Such double phase space (x-p) can be also for a harmonic oscillator. But, at a harmonic oscillator we cannot have two ellipses (or a circle and an ellipse) which touch on some points, but have the...

If I have a particle with: Momentum: p Spin: s Energy: E Position: x Time coordinate: t Charge: q And I preform a CPT transformation on said particle, what will these variables become? Can you show me mathematically? Also, could you show me how this effects the wavefunction/quantum state of...

hilbert2 submitted a new PF Insights post Damped Motion in Classical and Quantum Mechanics Continue reading the Original PF Insights Post.

Why or why not?

I am not a physicist by trade nor do I have any experience other than what I've read over the past few years. I once read a book by Stephen Hawking or Michio Kaku (or maybe Brian Green, I can't remember) in which they said something to the effect of "even if we had the technology to see down to...

How come a+a- ψn = nψn ? This is eq. 2.65 of Griffith, Introduction to Quantum Mechanics, 2e. I followed the previous operation from the following analysis but I cannot get anywhere with this statement. Kindly help me with it. Thank you for your time.

I am self studying the Book- Introduction to Quantum Mechanics , 2e. Griffith. Page 47. While the book has given a proof for eq. 2.64 but its not very ellaborate Integral(infinity,-infinity) [f*(a±g(x)).dx] = Integral(infinity,-infinity) [(a±f)* g(x).dx] . It would be great help if somebody...

In a recent article by BBM in Physical Review Letters highlights another approach to link QM to Zeta to Prove R.H. There approach proved unsuccessful. I want to ask professional Physicists if the following new approach have merit in connecting the Zeta function to QM? This new line of attack...

Hey guys, Am facing an issue, we know that x and y operators take the same form due to isotropy of space, but sir if we destroy the isotropy, then what form will it take? Can u pleases throw some light on this! Thanks in advance

I've recently been wondering about the notion of measurement in quantum mechanics. While I'm aware that understanding and precisely defining the concept of a quantum mechanical measurement is at the heart of interpreting the subject, I would like some feedback on some aspects of this topic I...

Homework Statement At t=0, the system is in the state . What is the expectation value of the energy at t=0? I'm not sure if this is straight forward scalar multiplication, surprised if it was, but we didn't cover this in class really, just glossed through it. If someone could walk me through...

Just curious if any of you out there who have completely different fields study this topic just for the joy of it. It seems like you would have to be pretty motivated or extremely intelligent to master these concepts for leisure.

Homework Statement Hi, I'm trying to self-study quantum mechanics, with a special interest for the group-theoretical aspect of it. I found in the internet some lecture notes from Professor Woit that I fouund interesting, so I decided to use them as my guide. Unfortunately I'm now stuck at a...

If I understand the many worlds QM interpretation correctly, for every quantum event the universe divides. However not all quantum events have a 50/50 probability. How does the many worlds interpretation deal with quantum events that have,say a 1/3 2/3 probability split?

Homework Statement I have some doubts about the method constructing chemical reaction process of quantum mechanics in the referencehttp://www.southampton.ac.uk/assets/centresresearch/documents/compchem/DFT_L2.pdf, for the example of ##H_2O## molecular dissociation to ##H^+## and ##OH^-## ions...

Hi, I'm preparing for an exam, and I'm going over past papers. I've solved parts a & b of this question without any problems, however I'm finding it hard to understand part c. I thought of shifting the boundary conditions so I'd have 0 and L in the place of ± L/2, but that would not work...

What is Cn in quantum mechanics?

I'm reading the book "Quantum Field Theory and the Standard Model" by Matthew Schwartz and I'm finding it quite hard to understand one derivation he does. It is actually short - two pages - so I find it instructive to post the pages here: The point is that the author is doing this derivation...

Hello! I just started reading a book about QFT by Peskin (it was recommended by one of my physics professor and I saw that MIT course on QFT also uses it). However they start right away with Klein-Gordon equation suggesting that I should be familiar with it. I took 2 classes on quantum mechanics...

Hello! I read that, according to quantum mechanics, any physical process must happen with a certain probability if it is not forbidden by symmetry/conservation laws. And now I just started an internship at the CMS aiming to find a Higgs like particle with mass higher that 125 GeV. And we have...

To what extent is quantum mechanics needed to explain the properties of water? Thanks in advance.

What I know: A ripple/wave in a field gives rise to a particle. For example, a ripple in electric field creates a photon. Question: Is this the same principle as probability wave which when observed reveals a particle?

How would this operator be implemented physically if we had a quantum computer? In Grover's algorithm this magical operator is often called "phase inversion". Here is the operator from wiki: https://wikimedia.org/api/rest_v1/media/math/render/svg/07fb23bffa787430b084971c6a108a8f6ff6c2b3 It’s...

Hi all - apologies, I'm starting a new thread here for something buried at the end of another thread - but I think the topic of that thread had changed sufficiently to warrant a more succinct top-level post. Thanks very much to PeterDonis for his very useful answers in the previous thread...

I am afraid I have no enough competence to raise this topic. I should not have. Because of a very limited experience I cannot back up my arguments. Because of knowing mostly my own experience I should have not made generalizations. Because of not reading completely even one textbook of QM, I...

<Mentor's note: moved from a technical forum, therefore no template.> I'm long out of college and trying to teach myself QM out of Shankar's. I'm trying to understand the reasoning here because I think that I am missing something... 1.1.3 1) Do functions that vanish at the endpoints x=0 and...

ShayanJ submitted a new PF Insights post Entanglement Entropy - Part 1: Quantum Mechanics Continue reading the Original PF Insights Post.

In Shankars "Principle of Quantum Mechanics" in Chapter 4, page 122, he explains what the "Collapse of the State Vector" means. I get that upon measurement, the wave function can be written as a linear combination of the eigenvectors belonging to a operator which corresponds to the...

In quantum mechanics, the velocity field which governs phase space, takes the form \begin{equation} \boldsymbol{\mathcal{w}}=\begin{pmatrix}\partial_tx\\\partial_tp\end{pmatrix} =\frac{1}{W}\begin{pmatrix}J_x\\J_p\end{pmatrix}...

I'm trying to solve a problem where I am given a few matrices and asked to determine if they could be density matrices or not and if they are if they represent pure or mixed ensembles. In the case of mixed ensembles, I should find a decomposition in terms of a sum of pure ensembles. The matrix...