Wavefunction Definition and 585 Threads

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...

Would it make sense to say that the entire evolutionary history of the universal wavefunction could simply be a single, continuous moment of self-measurement? In other words, that the universe exists for no other reason than to be the apparatus that is always in the process of measuring its own...

I am trying to solve the following exercise. In a H atom the electron is in the state described by the wave function in spherical coordinates: \psi (r, \theta, \phi) = e^{i \phi}e^{-(r/a)^2(1- \mu\ cos^2\ \theta)} With a and \mu positive real parameters. Tell what are the possible values...

I looked in the instructor solutions, which are given by: But I don't quite understand the solution, so I hope you can help me understand it. First. Why do we even know we are working with wavefunctions with the quantum numbers n,l,m? Don't we only get these quantum numbers if the particles...

Using the boundary conditions where psi is 0, I found that k = n*pi/a, since sin(x) is zero when k*a = 0. I set up my normalization integral as follows: A^2 * integral from 0 to a of (((exp(ikx) - exp(-ikx))*(exp(-ikx) - exp(ikx)) dx) = 1 After simplifying, and accounting for the fact that...

I’m new in QM. I have a simple question: when one says that the wavefunction collapses, is it the same as saying that the variance of an observable is 0? Thanks.

Part a: Using the above equation. I got $$\psi(x) = \int_{-\infty}^{\infty} \frac{Ne^{ikx}}{k^2 + \alpha^2}dk $$ So basically I needed to solve above integral to get the wave function. To solve it, I used Jordan's Lemma & Cauchy Residue Theorem. And obtained $$\psi(x) = \frac {N \pi...

The answer is no and even when decoherence occurs for Wigner's Friend in the lab, quantum coherence remains. Let's start with the paper that illustrates this. Assisted Macroscopic Quantumness CONT. https://arxiv.org/abs/1711.10498 Wow, I recently read this paper and the results are simply...

In the framework of tight binding approximation, does the wavefunction for atom A (or B) has two spinorial components(2 components) in "real space"? If so how does this spinorial component propagate in the graphene?

Some rotational quantum states are not allowed for a rotating particle. At quantum level, these "forbidden" quantum states is based on the requirement of the total wavefunction being either symmetrical or anti-symmetrical, depending on whether the particle is a fermion or boson. The particle's...

I have a basic question in elementary quantum mechanics: Consider the Hamiltonian $$H = -\frac{\hbar^2}{2m}\partial^2_x - V_0 \delta(x),$$ where ##\delta(x)## is the Dirac function. The eigen wave functions can have an odd or even parity under inversion. Amongst the even-parity wave functions...

If you look at the recent Wigner's Friend experiment, it seems to support Carlo Rovelli's Relational Interpretation which says there's no real measurement. Wiger's Friend carries out a polarization measurement. Before he does, the quantum system is in a superposition of horizontal/vertical...

This is what I have so far: $$ |\alpha\Psi_1 + \beta\Psi_2|^2 = |\alpha|^2|\Psi_1|^2 + |\beta|^2|\Psi_2|^2 + \alpha^*\beta\Psi_1^*\Psi_2 + \alpha\beta^*\Psi_1\Psi_2^* $$ $$=> |\alpha\Psi_1 + \beta\Psi_2|^2 = |\alpha|^2|\Psi_1|^2 + |\beta|^2|\Psi_2|^2 + 2Re(\alpha^*\beta\Psi_1^*\Psi_2) $$ I am...

Einstein condensate state or ultra hot fully ionized, removed of all-electron, plasma that is compressed like possibly something like fusion, state (an extraordinarily unattainable state currently; like compressed air into a liquid, but a solid; while even metallic hydrogen is, as far as I know...

I would differentiate this twice and plug it into the S.E, but for that I'll need E. Which I don't have. Please provide me some direction.

I would like to see what the shape of the ground state radial wavefunction for the Lithium atom is. An approximate function that shows the shape would be fine. Thanks.

Hello! I am a bit confused by the quantum numbers used to describe the rotation of a nucleus. In Wong's book these are J, M and K, which represent the rotational quantum number, its projection along the lab z-axis and its projection along the body intrinsic symmetry axis, respectively. However...

Suppose ##\psi_{0}## is a properly normalised wavefunction with ##<x_{\psi_0} >## = ##x_{0}## and ##<p_{\psi_0} >## = ##p_{0}##. Define a new wavefunction ##\psi_{new}##(x) = ##e^{{-iqx}/{\hbar}}## ##\psi_{0}## What is the expectation value ##<\psi_{new}>## in the state given by...

I'm trying to understand equation 209 on page 81 here: https://arxiv.org/pdf/1204.4325.pdf Here's what I understand so far: - We are to imagine a system in a superposition of |X> and |X'>, where these describe distinct particle configurations. - On the RHS of the eqn, the first term is...

Hey guys! New to the forums so unsure if this is exactly the right place to present this idea I have. I hope that you will find it interesting. I am all too familiar with claims of quantum consciousness woo. I am also aware that the role of 'wave function collapse', if such a thing even...

For instance, in the case of the infinite square well, the wavelength of the wavefunction is \frac{2L}{n}. This also turns out to be the De Broglie wavelength, and and we can find the possible energies directly from the Schrodinger equation, or by using the De Broglie relations. However, if the...

Is wavefunction always analytic signal? Is imagnigray part of wavefunction hilbert transform of real part of wavefunction?

Hi folks, I'm trying to get a grasp on some of the basic concepts of QFT. Specifically, I'm trying to picture what are the actual fields of QFT and how they relate to wavefunctions. There are already many helpful posts about those concepts, here and in other places, but some points are fuzzy...

I saw a paper on an experiment where a pump beam first went through a double-slit, then was downconverted with BBO. Recently a friend with a PhD in quantum physics said the downconversion will cause the pump's wavefunction to collapse and the implication for this experiment is that the pump...

Hello Physics Forum, I am not sure what to to in this task, because the wavefunction is only given as A_0. Maybe someone can explain it to me. Thanks in Advance, B4ckflip

Suppose one measures the position of a photon without destroying it. From my understanding, the wavefunction of the photon should collapse, and will return to a more spread out state over time. How would one calculate this, specifically the rate at which the wavefunction spreads out from the center?

I have an issue trying to understand the derivation of equation 3.40 (screenshot attached) of Blundell's QFT book. Here's my attempt. ##| x,y \rangle = |x\rangle \otimes |y\rangle = \Big( \int dp' \phi_{p'}(x)|p'\rangle \Big) \otimes \Big( \int dq' \phi_{q'}(y)|q'\rangle \Big)## which gives...

Should I treat ψ1 as ψ and ψ 2 as ψ*?

We are given the wave function with spin, but it doesn't say in which Ylm each spin X± goes. So how do I know? Examples; (1) Ψ = 1/√3 R21(r) ( Y10 √2Y11 ) Here we have the up Spin X+ to Y10 and the X- to Y11 I notice the X- went to...

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...

Suppose that the spacetime is discrete, with only certain positions being possible for any particle. In this case, the probability distributions of particles have nonzero values at the points on which the wavefunction is defined. Do we need randomness in the transitions of particles in such a...

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...

I have read Lubos Motl blogposts (https://motls.blogspot.com/2012/11/why-subjective-quantum-mechanics-allows.html and https://motls.blogspot.com/2019/03/occams-razor-and-unreality-of-wave.html) stating that the wavefunction is subjective. This means that it is perfectly valid that two different...

I am not sure whether I have differentiated correctly $$\frac{\partial\Psi(x-ut,t)}{\partial t}=-u\frac{\partial\Psi(x-ut,t)}{\partial(x-ut)}+\frac{\partial\Psi(x-ut,t)}{\partial t}$$ and $$\frac{\partial^2\Psi(x-ut,t)}{\partial x^2}=\frac{\partial^2\Psi(x-ut,t)}{\partial(x-ut)^2}$$ So, we...

Look at the paper in the link below: https://link.springer.com/content/pdf/10.1007%2Fs10701-016-0026-7.pdf It introduces a pilot-wave model on a discrete spacetime lattice. However, the pilot-wave model is not deterministic; the motion of quantum particles is described by a |Ψ|^2-distributed...

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 have question, how can I solve problem of particle in rigid box when one of the wall gets completely destroyed? At time t = 0 the right wall of box gets completely destroyed, left wall is still here( ψ(0) = 0 ), also at t = 0 we know that particle is in ground state. How can I search for...

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...

I am reading a textbook quantum physics by stephen gasiorowicz. And he defines a wavefunction in this form, $$Ψ(x,t)=\int_{-∞}^{∞}A(k)e^{i:(kx-ωt)}dk$$ I did not understand why its a function of ##k## or why even we are taking integral with respect to ##k## ? Is ##k## actually means momentum...

Homework Statement Let us suppose we have a particle with energy ##E## and ##E<U## and the potential defined as ##U(x)=0## for ##x<0## (I) ##U(x)=U## for ##0<x<L## (II) ##U(x)=U_0## for ##x>L## (III) In this case ##E>U_0## and ##U>U_0## Homework Equations $$HΨ=EΨ$$ The Attempt at a...

Hi. In infinite volume a normalizable wavefunction → 0 as r or x,y,z→ 0 but do all the derivatives and higher derivatives → 0 as well ? Thanks

Homework Statement Consider the state $$\psi_\alpha = Ne^{\alpha \hat a^\dagger}\phi_0, $$ where ##\alpha## can be complex, and ##N = e^{-\frac{1}{2}|\alpha|^2}## normalizes ##\psi_\alpha##. Find ##\hat N \psi_\alpha##. Homework Equations $$\hat N = \hat a^\dagger \hat a$$ $$\hat a\phi_n =...

Hi . For a system such as an infinite well or a harmonic oscillator if the energy is measured and it returns a value , say E1 corresponding to the ket | 1 > then this evolves according to exp( -iE1t/ħ) | 1 >. So this means that for any time >0 a measurement of the system will always give the...

Hi, I'm sorry if this question has already been answered somewhere and I'm just too incompetent to find it, buuut: As the title already says, I really do not get that part of quantum physics (if you can even say I'm getting ANY part at all...). As I searched all Google for an answer I just...

Homework Statement A particle of mass m in one dimension has a potential: $$V(x) = \begin{cases} V_0 & x > 0 \\ 0 & x \leq 0 \end{cases} $$ Find ##\psi(x)## for energies ##0 < E < V_0##, with parameters $$k^2 = \frac{2mE}{\hbar^2}$$ and $$\kappa^2 = \frac{2m(V_0 - E)}{\hbar^2}$$...

Homework Statement How should I calculate the expectation value of momentum of an electron in the ground state in hydrogen atom. Homework Equations The Attempt at a Solution I am trying to apply the p operator i.e. ##-ihd/dx## over ##\psi##. and integrating it from 0 to infinity. The answer I...

I have read that the integral of d3x ∇(ψ*ψ) is zero because the total derivative vanishes if ψ is normalizable. Does this mean that the integral of d3x ∇(ψ*ψ) is ψ*ψ evaluated at the limits where ψ is zero ? Thanks

Radio waves are usually not viewed as streams of photons but according to quantum mechanics that is exactly what they are. But what does the wavefunction of an RF photon look like? If we consider a dipole radiator, say of 10 Mhz, that emits a single photon, my guess is that the wavefunction of...

...to give a number? https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2016/lecture-notes/MIT8_04S16_LecNotes5.pdf On page 6, it says, " Matrix mechanics, was worked out in 1925 by Werner Heisenberg and clarified by Max Born and Pascual Jordan. Note that, if we were to write xˆ...