Wavefunction Definition and 585 Threads

How do i sketch a psi function when there is no sinus or cosinus i see sometimes its curving but sometimes its directly going down when reaching the top whats the decisive factor here to sketch a graph.

I'm teaching Quantum mechanics to freshmen in my college, but I'm stuck on a very basic concept that I always took for granted. I'm a chemist major, not a physicist, but I thought it's something I should clearly understand. I am embarrassed to ask this question, but I'd rather be embarrassed now...

Hello! I am asking this question from a molecular physics perspective (i.e. diatomic molecule placed in an external electric field), but it's quite general in terms of the formulation. I have a 2 level system (call the levels ##\ket{0}## and ##\ket{1}##) that can be connected by an electric...

I've seen the hydrogen electron's wavefunction expressed in the basis ##\ket{n l s m_l m_s}## or ##\ket{n l s j m_j}##, but so far, never in ##\ket{n l s m_l m_j}##. My question is, are certain combinations of quantum numbers, eg, ##\ket{n l s m_l m_j}##, forbidden? If ##\ket{n l s m_l m_j}##...

Hi, when normalising the wavefunction I get two answers. Is this correct? My notes only has 1/sqrt(L) = A.

The first equation states that every wavefunction can be written as a sum of wavefunctions of definite momentum, with A_p being defined as the coefficients in the expansion such that when you take the |wavefunction|^2 it equals 1 - fine. We then multiply by the wavefunction conjugate and...

Since ##U## is a space and spin rotation, it would be $$U(R) = e^{-i\textbf{L}\cdot \hat{\textbf{n}}\phi/\hbar}\cdot e^{-i\textbf{S}\cdot \hat{\textbf{n}}\phi/\hbar}$$ And, then $$\psi'(\textbf{r}, m) = \langle\textbf{r}, m|e^{-i\phi(\textbf{L} + \textbf{S}) \cdot...

"However, accurate quantum-mechanical calculations (starting in the 1970s)... singly occupied orbitals are less effectively screened or shielded from the nucleus, so that such orbitals contract and electron–nucleus attraction energy becomes greater in magnitude (or decreases algebraically)."...

Hello All, 2nd year undergrad taking my first course in modern physics. We have been given this question in a mock exam and at the bottom is the solution. When looking at a general cubit it seems the argument of both sin and cos functions should be (pi/2) not (pi/3). I have figured out a...

I was thinking about this paper (https://arxiv.org/abs/1405.0298) where the authors argue that there wouldn't be dynamical quantum fluctuations in a De Sitter space as fluctuations would be static once all perturbative radiation escapes the horizon (in the case that the Universe has a finite...

When studying the hydrogen atom, given that the potential depends only on the distance and not an any angle, we can do a separation of variables of the wavefunction as the product between a function depending only on the distance between particles (protons and electrons) and a spherical...

And then, if the wavefunction does collapse as the electron binds to the proton, is that collapse temporary, or will the wavefunction remain collapsed until the electron escapes and is free again? Or, will the wavefunction of a freshly bound electron eventually return to a max superposition...

What are the implications that the wavefunction is not Lorentz invariant?

What is ##<x|P|x'>##? (for particle in 1d, and ##\hbar = 1##)?\begin{align*} <x|P|x'> &= \int dp' <x|P|p'><p'|x'> \\ &= \int dp' \ p' <x|p'> <p'|x'> \\ &= \int dp' \ p' \frac{1}{\sqrt{2\pi}} e^{ip'x} \frac{1}{\sqrt{2\pi}} e^{-ip'x'} \\ &= \frac{1}{2\pi} \int dp' \ p' e^{ip'(x-x')} \end{align*}

My understanding is: $$\phi (\mathbf{k})=\int{d^3}\mathbf{x}\phi (\mathbf{x})e^{-i\mathbf{k}\cdot \mathbf{x}}$$ But what is ##\phi (\mathbf{x})## in Qft? In quantum mechanics, $$|\phi \rangle =\int{d^3}\mathbf{x}\phi (\mathbf{x})\left| \mathbf{x} \right> =\int{d^3}\mathbf{k}\phi...

(For me to understand, please be mindful to avoid a bunch of jargon) I'm not sure if the proper word is wavefunction or superposition, and didn't find anything in a search of the difference between the two. So will elaborate on the question in my own words. To begin, as far as I undestand...

In this 2011 paper, Lundeen & colleagues used weak measurement to map both imaginary and real components of a wavefunction directly, without destroying the state. It says: “with weak measurements, it’s possible to learn something about the wavefunction without completely destroying it”. And...

I was reading an article 'What Einstein Really Thought about Quantum Mechanics' in Scientific American. There they mentioned something I didn't know - Bohr did not believe in Wave Function Collapse as an issue (I don't either - but that's just my opinion, so means nothing). I found this...

The Maxwell wavefunction of a photon is given in [here] as follows: Because the curl operation mixes 3 different components, this wavefunction only works for a minimum of 3 space dimensions, with each grid point having 6 component numbers ##{E^1, E^2, E^3, B^1, B^2, B^3}##, and with the...

Normalize function f(r) = Nexp{-alpha*r} Where alpha is positive const and r is a vector I was just wondering if the fact that we have a vector value in our equation changes anything about the solution

i have use time evolution operator to get the wavefunction at any time "t" as Ψ(x,t) = U(t,t1) * Ψ(x,t1) but i don't know how to calculate next part of the question

Hello, I hope you are well. I have been doing a lot of readings on the wavefunction and have a question I did not see asked anywhere else in these forums. I was wondering if someone could shed some light on this for me? I know the wavefunction is in 3N coordinate space and could be used to...

Quantum states are most often described by the wavefunction ,##\Psi##. Variable ,##\Psi(x_1x_2\dots x_n) \Psi^*(x_1x_2\dots x_n)## defines probability density function of the system. Quantum states can also be described by the density matrices (operators). For a pure state, density matrix is...

I understand that the uncertainty is low when you're dealing with a "macro" scale area that is much bigger than Planck's constant. But what's confusing to me is when you know with extreme precision the location, but there's so many particles involved that there is little uncertainty since the...

I can understand how ##\phi (x)|0\rangle## represents the wavefunction of a single boson localised near ##x##.I don't understand how the same logic appies to ##A^{\mu}(x)|0\rangle## and ##\psi |0\rangle##. Both of these operators return a four component wavefunction when operated on the vaccuum...

If we had a system of ##N## non – interacting electrons than a wavefunction of such a system is a product of one-electron wavefunctions otherwise known as a Hartree product: $$ \Psi(x_1,x_2,...,x_N) = \prod_{n=1}^N \psi(x_n) $$ This means that in such a hypothetical system , it is possible to...

At what point does the electron become ionized in the hydrogen atom solution

I am considering tunnel effect with a potential barrier of a certain height that is ##\neq 0## only for ##0 \le x \le a## . I write the Hamiltonian eigenfunctions outside the barrier as:## \psi_E(x)=\begin{cases} e^{ikx}+Ae^{-ikx} \quad \quad x \le0 \\ Ce^{ikx} \quad \quad x\ge a \\...

I ran into this question in my problem sheet. Does anybody know how to work it out?

So I have come up with my solution(attempt) which is: where ( $$\psi_ 1 \triangleq Asin(kx),0<x<L$$ $$\psi_ 2 \triangleq Be^{-sx},x>L$$ $$k \triangleq \sqrt{\frac{2mE}{\hbar^2}} $$ $$s \triangleq \sqrt{\frac{2m(V-E)}{\hbar^2}} $$) But this has a serious problem about boundary: I think...

Hello there, for the above problem the wavefunctions can be shown to be: $$\psi_{n,l}=\left[ \frac {b}{2\pi l_b^2} \frac{n!}{2^l(n+l)!}\right]^{\frac12} \exp{(-il\theta - \frac {r^2\sqrt{b}}{4l_b^2})} \left( \frac {r\sqrt{b}}{l_b}\right)^lL_n^l(\frac {r^2b}{4l_b^2})$$ Here ##b = \sqrt{1 +...

The wavefunction of ##|\psi\rangle## is given by the bra ket ##\psi (x,y,z)= \langle r| \psi\rangle## I can convert the wavefunction from Cartesian to polar and have the wavefunction as ## \psi (r,\theta,\phi)## What bra should act on the ket ##|\psi\rangle## to give me the wavefunction as ##...

We've a two interacting particle system, with Hamiltonian as: ##H_{s y s}=\frac{\mathbf{p}_{1}^{2}}{2 m_{1}}+\frac{\mathbf{p}_{2}^{2}}{2 m_{2}}+V\left(\mathbf{r}_{1}, \mathbf{r}_{2}\right)## we reduce it to two non interacting fictitious particles,one moving freely other in a central field...

If ##\psi(x, t)=\left(\frac{1}{2 \pi \alpha^{2}}\right)^{1 / 4} \frac{1}{\sqrt{\gamma}} e^{i p_{0}\left(x-p_{0} t / 2 m\right) / \hbar} e^{-\left(x-p_{0} t / m\right)^{2} / 4 \alpha^{2} \gamma}##where * ##\gamma=1+\frac{i t} {\tau}##( a complex number) * ##\tau=\frac{m h}{2...

I've a Gaussian momentum space wavefunction as ##\phi(p)=\left(\frac{1}{2 \pi \beta^{2}}\right)^{1 / 4} e^{-\left(p-p_{0}\right)^{2} / 4 \beta^{2}}## So that ##|\phi(p)|^{2}=\frac{e^{-\left(p-p_{0}\right)^{2} / 2 \beta^{2}}}{\beta \sqrt{2 \pi}}## Also then ##\psi(x, t)=\frac{1}{\sqrt{2 \pi...

For the free particle in QM, the energy and momentum eigenstates are not physically realizable since they are not square integrable. So in that sense a particle cannot have a definite energy or momentum. What happens during measurement of say momentum or energy ? So we measure some...

My Bachelor thesis is all around Excitons (specifially transitions between excitons of different energies). During my work I often had trouble with the spin and the wavefunction of them. Is there maybe some good (free) literature about the theory of excitons ? I found some books in the internet...

-1st: Could someone give me some insight on what a ket-state refers to when dealing with a field? To my understand it tells us the probability amplitude of having each excitation at any spacetime point, but I don't know if this is accurate. Also, we solve the free field equation not for this...

Summary:: We are currently studying basics of quantum mechanics. I'm getting the theory part but it's hard to visualise everything and understand. We are given this question to plot the function so if someone could help me in this. Plot the following function and the corresponding g²(x) g(x)...

What is the difference between an absolutely continuously differentiable function and a wave? Are all absolutely continuously differentiable equations waves?

The goal I am trying to achieve is to determine the momentum (2D) in a quantum system from the wavefunction values and the eigenergies. How would I go about this in a general manner? Any pointers to resources would be helpfull.

Hi. I would love if someone could check my solution since me and the answer sheet I found online don't agree. The probability is given by the triple integral \begin{align*} \int_0^{r_b} \int_0^{2\pi} \int_0^\pi |\psi (r)|^2 r^2 \sin{\theta} \,d\theta \,d\phi \,dr &= \frac{1}{\pi...

I've heard that the wavefunction as a function of x has units of square root of inverse distance, but I haven't heard an intuitive description of why this is aside from that the math works out when you integrate to get the probability. But aside from the math working out, I'm hoping to get a...

The linear combination of the eigenfunctions gives solution to the Schrodinger equation. For a system with time independent Hamiltonian the Schrodinger Equation reduces to the Time independent Schrodinger equation(TISE), so this linear combination should be a solution of the TISE. It is not...

To me, the ##K## obtained by solving the Schrodinger equation and the de broglie wavelength seem two completely unrelated quantities. Can someone explain why have we equated ##K## and ##\frac{2\pi}{\lambda}##. Also, isn't writing ##p = \hbar K## implying that eigenstate of energy is also an...

Background While watching Does time cause gravity? from PBS Spacetime, i wondered if its possible to "derive" the geodesic equation not from GR alone, but by assuming each particle is described by an extended wave function and the time evolution of this wave is not constant but the rate varies...

For normalizing this wave function, I began by finding the complex conjugate of psi and then multiplied it with the original psi. Now what I am getting is A^2 integral exp(2cx^2-4ax) dx = 1 Now I am not getting how to solve this exponential term. I tried by completing the square method but it is...

I tried writing the function as: Ѱ = c1Φ1 + C2𝚽2 + C3𝚽3 in order to then find mod C1^2... But ɸ = √2/a sin(ᴨx/a) and not sin(ᴨx/a) I cannot understand how the factor of "√2/a " comes

If an electomagnetic wave like blue light, for example, exists in 3 dimensions, then how does/can the AdS/CFT conjecture explain it's emergence? Are the electric and the magnetic components of the blue wave both in 2 dimensions in CFT, and if so how would they combine and emerge into AdS to form...

The Hawking-Hartle no boundary condition is well known. The authors considered a many worlds/histories model considering a sum over all compact euclidean metrics. But are there any models or theories that consider a sum over all possible metrics or boundaries? And finally, if all possible...