What is Quantum machenics: Definition and 36 Discussions

I was reading a section of The Physics off Quantum Mechanics by James Binney and David Skinner. On page 45, when discussing the probability current (in the wave mechanics formalism) in calculating it they state: I.e.$$ i \hbar \left( \psi^{*} \frac{\partial}{\partial t} \psi + \psi...

hi all how do I prove that $$ <A^{n}>=<A>^{n} $$ It seems intuitive but how do I rigorously prove it, My attempt was like , the LHS can be written as: $$ \bra{\Psi}\hat{A}.\hat{A}.\hat{A}...\ket{\Psi}=\lambda^{n} \bra{\Psi}\ket{\Psi}=\lambda^{n}\delta_{ii}=\lambda^{n} $$ and the RHS equal: $$...

For a state to be stationary it must be time independent. Naively, I tried to find the values of c where I don't have any time dependency. ##e^{c \cdot L_z} \psi (r,t) = e^{c L_z} \sqrt{\frac{8}{l^3}} sin(\frac{2 \pi x}{l}) sin(\frac{2 \pi u}{l}) sin(\frac{2 \pi z}{l}) e^{-iEt/\hbar}##...

Of course, this question consisted of two parts. In the first part, we needed to calculate the first-order correction. It was easy. In all the books on quantum mechanics I saw, only first-order examples have been solved. So I really do not know how to solve it. Please explain the solution method...

When we are talking about Bloch's theorem and also the tight-binding approximation, we can use them to help finding eigenstates of a system. However, I am so confused how to apply it in this case (below is my homework) and don't even know how to start it... All I understand about the Bloch's...

I've been assigned to do a problem from Landau which you can read below: I have no problem with finding the energy. Then I write down the equations: \begin{equation*} \begin{cases} (V_{11}-E^{(1)})|c_1|e^{i\alpha_1} + V_{21}e^{i\alpha_2}|c_2| = 0\\ V_{12}e^{i\alpha_1}|c_1| +...

Summary:: I have a problem with a particle, which gets scatterd at a double delta-potential Hello, I am really stuck with the floowing problem: A particle moves from the left along the x-axis and gets scatterd at a one-dimensional potential V(x)=a[dirac delta of x) +b [dirac delta of x-c]...

I observe that all bound states have discrete energy levels, eg. particle in a box, hydrogen atoms. But unbound states always have a continuous energy spectrum. For example, for the case of a finite potential well, when ##E<V_0##, we have discrete energy for the bound states. When ##E>V_0##, the...

According to this this the Darboux transformation preserves the discrete spectrum of the Haniltonian in quantum mechanics. Is there a proof for this? My best guess is that it has to do with the fact that $$Q^{\pm}$$ are ladder operators but I'm not sure.

For the region where V = 0, solving the schrodinger equation leads to the above value of wave function, psi = sqrt(2/L) sin(pi x/L) Since in the qus. it is not stated about the 'direction of movement' only restricted to +x direction, I think that the probability will be 1/2. And finding the...

Given that the Minkowski metric implies the Lorentz transformations and special relativity, why do the equations of relativistic quantum mechanics, i.e., the Dirac and Klein-Gordon equations, require a mass term to unite quantum mechanics and special relativity? Shouldn't their formulation in...

Can someone please tell me(and in simple terms-like in percentages), what the maximal violations of Bell's inequality has been recorded at in actual experiments and in an ideal scenario? Thank you.

hi. How to obtain the expected value of x in the momentum space ?

My problem is in (b) it written sketch psi (X,0) as function of X , why the answer was like this I didn't understand the branch from a to b Best

The pure energy released from antimatter annihilation can there be any use of this clean energy for research purposes like the use of light in LIGWO for gravitational waves study can we use it efficiently like light in LIGWO I think we can and it could lead us to reveal mysteries of universe

In https://en.wikipedia.org/wiki/Lamb_shift about the lamb shift, it's mentioned that the change in the electron's frequency due to QED effects (vacuum polarization and self-energy correction) is about 1 GHz, which would translate to an energy change of hf = 6.63E-25 J. This is 3E-7 times of the...

I have read on Wikipedia (https://en.wikipedia.org/wiki/Compton_wavelength) that we cannot measure the position of a particle more precise than half of its Compton wavelength, since the photon we would need will be so energetic to produce electron-positron pairs. How does the creation of...

I know that in some Bohmian papers (like https://arxiv.org/pdf/quant-ph/0303156.pdf), electron-positron pair creation and annihilation is modeled by different methods like stochastic jumps in the configuration space. My question is, is there any Bohmian approach to reproduce all of the...

Considering the quantum mechanical model for an atom, what exactly happens when two atoms (say, two Ca2+ ions in a Brownian motion) collide with each other? As I know, this collision is not like a regular elastic or inelastic collision between two macroscopic objects. Is it mainly due to the...

In https://arxiv.org/pdf/quant-ph/0203049.pdf, which is in the realm of Bohmian mechanics, Antony Valentini claims that by having a "non-equilibrium" particle with arbitrarily accurate "known" position, we can measure another particle's position with arbitrary precision, violating Heisenberg's...

A free electron, or any other quantum particle, has an uncertain position/momentum, according to Heisenberg uncertainty principle. The squared amplitude of the wavefunction determines the probability of finding the electron at any point of the space. Accordingly, atomic orbitals are attributed...

I am studying the deuterium's nucleus. As we know, there are just two eigenstates for a spin 1/2 particle: either spin up or spin down. Thus, over the whole nucleus, you get 4 possible combinations: 1) Spin up-spin up 2) Spin up-spin down 3) Spin down-spin up 4) Spin down-spin down If you...

In https://www.sciencedirect.com/science/article/pii/S0378437109010401, the author claims that the interference pattern obtained in the double-slit experiment does not need a wave description of matter, and can be accounted for by the "quantized momentum transfer" from the slits to the electron...

The videos from Veritasium explaining permanent static magnets and electromagnets were quite good I thought… But they have me a little confused with regard to the origins of magnetic fields generated by an electric current as opposed to a permanent static magnet from say iron. 1. An...

In http://www.feynmanlectures.caltech.edu/III_05.html#Ch5-S1, Feynman mentions that the 2-stage Stern-Gerlach experiment, which proves the electron spin states to be in a superposition, has never been actually done! I have also not seen any paper reporting such an experiment. My question is, has...

Could someone, in laymen's terms explain to me what stochastic mechanics is?

Homework Statement Three-state system. The nucleus of the nitrogen isotope 14N acts, in some ways, like a spinning, oblate sphere of positive charge. The nucleus has a spin of lft and an equatorial bulge; the latter produces an electric quadrupole moment. Consider such a nucleus to be spatially...

I was reading *Introduction to Nuclear Physics* by Krane and stumbled on the following (page 47): In Elastic scattering, the initial electron wave function is of the form ##e^{i k_i r}## (free particle of momentum ##p_i = \hbar k_i##). The scattered electron can also be regarded as a free...

I was reading the free will theorem and it basically says that subatomic particles and observers have to have free will because there's nothing prior to measurement that predetermines the outcome. Here's more: The free will theorem states: Given the axioms, if the two experimenters in question...

In https://arxiv.org/ftp/arxiv/papers/1409/1409.5158.pdf, the author (Donald A. Graft) concludes that Bell tests cannot refute local realism, because they employ a wrong analysis. He says: "The quantum joint prediction cannot be recovered in an experiment with separated (marginal) measurements...

Homework Statement Find the noralization constant ##A## of the function bellow: $$ \psi(x) = A e^\left(i k x -x^2 \right) \left[ 1 + e^\left(-i \alpha \right) \right], $$ ##\alpha## is also a constant. Homework Equations ##\int_{-\infty}^{\infty} e^\left(-\lambda x^2 \right) \, dx = \sqrt...

I had a question about Schrodinger's cat that extends to the universe. First, I'm sure everyone knows the Schrodinger's cat set up so I won't repeat it. I will just ask, how can the cat be dead or alive prior to measurement? This measurement would be either atoms in the radioactive substance...

I just confused about it.Why can't we discribe a particle just one wave function instead of wave packet(group of waves with different phase velocities)?

Hey, I am currently reading over the linear algebra section of the "introduction to quantum mechanics" by Griffiths, in the Inner product he notes: "The inner product of two vector can be written very neatly in terms of their components: <a|B>=a1* B1 + a2* B ... " He also took upon the...

The analytical solutions are: \begin{equation} \psi(x) = \begin{cases} Ce^{\alpha x}, \text{if } x < -\frac{L}{2}\\ Asin(kx) + Bcos(kx), \text{if } -\frac{L}{2} \leq x \leq \frac{L}{2}\\ Fe^{-\alpha x} , \text{if } x > \frac{L}{2} \end{cases} \end{equation}...

Griffith says in problem 1.15 the potential energy has an imaginary part. my question is that any real case exists where the part of the potential energy is imaginary?