Questions tagged [wavefunction]
A complex scalar field that describes a quantum mechanical system. The square of the modulus of the wave function gives the probability of the system to be found in a particular state. DO NOT USE THIS TAG for classical waves.
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A classical localization of a wave function?
We know that the state of a quantum particle defined on the real line is represented by its wave function $\psi(x)$ that is the position probability amplitude. We also know that the momentum ...
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Why do most introductory texts on QM use the Schrödinger formulation rather than Heisenberg's matrix mechanics? [closed]
I know they're mathematically equivalent, and that makes intuitive sense, seeing as linear differential equations can in general be solved using matrices and other linear algebra approaches. In fact, ...
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Momentum Space Solutions of the 1D Schrodinger equation in the Potential $f(t)x$ [closed]
Yesterday, I asked a question about solving the 1D Schrodinger equation in a time varying potential $f(t)x$ using a method solely in configuration space. Although this approach does not directly ...
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Basis representation for isotropic 2D quantum harmonic oscillator
The basis functions of the 2D isotropic quantum harmonic oscillator are of the form
$$ \psi_{n,\ell} (r,\varphi) = A_{n\ell}(r)e^{i\ell\varphi}$$
where $A_{n\ell}(r) = \frac{\sqrt{2 \times p!}}{\sqrt{(...
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Problem on deep potential well [closed]
The problem is to find out the Schrödinger equation for a system of two particles $m_1$ and $m_2$ confined in a one dimensional well.
I have previously solved the problem of a single particle in a one ...
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Solving the 1D Schrödinger equation under the potential $V(x) = f(t)x$ [closed]
Following the sketch given in this answer, I hoped to solve the 1+1 dimensional Schrodinger equation under a potential $f(t)x$ by using a time dependent boost.
$$\left(\frac{-\hbar^2}{2m}\frac{\...
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Are expectation values for any hermitian operator, well defined in case of scattering states, or rather non-normalizable states?
Consider I have the following commutator, $[H,O]$ where $O$ is some hermitian operator.
I know that if $$H|\psi\rangle=E|\psi\rangle$$
Where $|\psi\rangle$ represents the bound energy eigenkets, for ...
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Ground state of hydrogen atom, $e^{-\kappa r }$ or $e^{-\kappa r }/ r$
The ground state must be an $s$-wave state, so it depends only on the radius $r$. I cannot remember the exact form, but I know it must be one of the two.
Is there any simple way to determine which one ...
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Why can I ignore $R(\rho)$?
The question is 12.3.3 from Shankar. Consider a particle with the wave function $\psi(\rho, \varphi) = Ae^{-\rho^2/2\Delta^2}\cos^2(\varphi)$, and show $\mathbb{P}(l_z = 0) = 2/3$.
We have just found ...
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Visualizing excitonic wavefunctions
I was reading this article about exciton dynamics in Photosystem II of plants when I came across the following passage describing the exciton wavefunction for a coupled dimer of molecules $1$ and $2$ ...
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Does a generic wave function always return to a symmetric state?
I'm reading about the infinite square well, and I've thought if a generic wave function that evolves under the hamiltonian can return to a state s.t.
$\psi (x, \tau) = \psi (-x,0)$,
where $\tau$ is ...
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Objection to interpretation of quantum mechanical wave function being wave
I am currently studying Quantum mechanics (first time) from Ballentine's book. In Chapter 4, he objects the idea of associating wave functions, which are solutions of Schrödinger equation in position ...
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How does a state change in time for a free particle?
I was reading my textbook and there was this question: For the fundamental state of an infinite square well:
$$ \left| \psi \right \rangle = \sqrt {\frac{2}{L}} \sin \left( \frac{\pi x}{L} \right)$$
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What are Test Functions in QFT (physics context)?
In terms of mode function solutions of the KG equation, the field operator can be written as
$$ \hat{\phi}(x) = \int_{R^3} d^3\textbf{p}\space \left(u_\textbf{p} \hat{a}_\textbf{p}+ u^*_\textbf{p}\hat{...
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Examples when wavefunction is changing but probability density is constant?
What are examples of wavefunction that changes with time but the square of wavefunction is constant?
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In a finite quantum well with a constant electric field, is it possible to find a bound state? [closed]
You have this equation
$-\frac{\hbar}{2m}\frac{\partial^2 \Psi}{\partial x^2}+(V(x)-eFx)\Psi=E \Psi$ where $V(x)$ is the potential for a finite quantum well.
Is there solution which is a real bound ...
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Dirac Formalism/Notation Question
I'm reading the 3rd edition of Sakurai and Napolitano's Modern Quantum Mechanics, which (probably rightly) relegates wave mechanics to an appendix. Instead, it carefully develops Dirac's formalism, ...
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What is the mathematical relationship between the wave functions of QM and the fields in QFT?
To be more specific, say I have the wavefunction for the position of some arbitrary particle, but then I also have the QFT operator (is that the correct term?) modeling the position of that same ...
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How much does the collapse of the wave function reveal about the state of the quantum prior to collapse?
The best way I can pose this question is through an example: suppose a photon passes through a beamsplitter, putting the photon into a superposition of the two paths (reflected or passed through), and ...
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What happens step-by-step (and why) when a particle tries to escape an infinite potential well?
I am aware that the following question might be quite elementary. My background is mainly in mathematics and my physics education is limited to high-school level material (discounting analogues made ...
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Construction of the wave function of $D$ mesons
The $D^{\ast+}$ meson can decay as $D^0+\pi^+$ or as $D^++\pi^0$. It is a vector meson, therefore having $J^P=1^-$. Furthermore, $D^+$ is made of $c\overline d$ and $D^0$ of $c\overline u$. The ...
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Which continuous functions that vanish at $\pm$ infinity are not square-integrable? [closed]
What is the condition for a continuous real-valued function which is zero at $\pm \infty$ to be not square-integrable?
By "not square-integrable" I mean functions $f(x)$ such that $\int_{-\...
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What's the derivative of the wave function of hydrogen atom? [closed]
I'm trying to solve a quantum mechanics exercise.
I've got the wave function:
$$\psi(\vec{r})=\phi_{n,l,m}\left(\vec{r}\right)e^{\frac{iqx}{\hbar}}$$
where $\phi_{n,l,m}\left(\vec{r}\right)$ is the ...
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Difference between a quantum wavefunction and a wave
When reading about quantum wavefunctions, I understood that different subshells have different "shapes" of orbitals, which describe the probability density of the electron. The orbital "...
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What does the $\Delta x $ in Heisenberg uncertainty principle actually mean?
In the textbook ''Concepts of Modern Physics -Arthur Beiser'' in chapter 3 section 3.7 where the book talks about the uncertainty princple
While illustrating the physics behind the uncertainty ...
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Quantum state in continuous basis [duplicate]
If I have an arbitrary state $|\psi\rangle$ and want to represent it in a continuous basis, for example the position basis in $x$-direction, I will get
$$|\psi\rangle = \int dx\, \langle x|\psi\rangle|...
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Why is Griffiths using ordinary power series to solve Hydrogen atom problem?
The hydrogen atom problem leads to a differential equation of the form
$$\rho\frac{d^2v}{d\rho^2}+2(\ell+1-\rho)\frac{dv}{d\rho}+[\rho_0-2(\ell+1)]v=0\tag{4.61}$$ where $\rho_0$ is a constant. In ...
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What does the wavefunction column mean in the Dirac equation?
I'm having trouble understanding what does the column wavefunction - with 4 components - in the Dirac equation really mean (physically). How does an operator, say, the momentum operator, act on the ...
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Does an electron's wave function collapse when it emits a photon?
I've been wondering how electromagnetic interactions between electrons are calculated if the position isn't determined until the wavefunction describing position collapses.
Does the wavefunction need ...
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Is the QED equation of motion for the wavefunction just the Dirac equation?
In the QED wiki article, they derive the equation of motion under the Lagrangian, using the classical Euler-Lagrange equation. This gives
$$(i\gamma^\mu\partial_\mu - m)\psi = e\gamma^\mu A_\mu\psi.$$...
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When do we exclude non-normalizable solutions and when not?
I'm a bit confused on when we should keep any non-normalizable solutions and when not. What do I mean?
Let's say that we have the free particle system. The energy eigenstates are not normalizable - ...
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Are the probability amplitudes in the continuous case, always the coefficients of the eigenstates of the wave-fun. expansion?
Assume that we have a Hamiltonian eigenvalue problem with continuous energy eigenvalues $E$. Griffiths says that the inner product of an eigenstate $ψ$ with the total wavefunction $Ψ$ gives the ...
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Intuitive and/or qualitative meaning of Heisenberg's uncertainty principle
I'm trying to figure out what uncertainty principle really means, and I'm arrived to construct this 'mental experiment': let's suppose to know whit great precision the momentum of an electron (or any ...
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How to prove the bound and scattering states theorem? [duplicate]
In Griffiths it is mentioned that if the energy eigenvalue is less than the value of the potential at + and - infinity, then we have bound states. If however the energy is bigger than the potential at ...
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When solving the Schrodinger Equation, where do we add the condition that $E$ is real?
I'm reading through Griffiths, and I noticed two seemingly contradictory facts:
In Chapter 1, it is proved that for any square-integrable function solving the Schrodinger Equation, $$\frac{d}{dt}\...
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Local conservation law of the Pauli current density
Is there a reference for local conservation of the Pauli current density, i.e.
$$J = \Im(\overline{\psi}(\nabla-iA)\psi) - \nabla \times (\overline{\psi} {\sigma} \psi) $$
where $\psi = (\psi_1,\psi_2)...
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In slit experiment: is it one wave function before and two wave functions after the split?
Forgive my round-about background to the question: I'm curious how the experiment "fires electrons slowly that interact with themselves"... I'm thinking that's just a simplification?
I feel ...
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Can Maxwell's electromagnetic vector field be simplified to a scalar field?
Maxwell's electromagnetism essentially associates 6 numbers $[E_x, E_y, E_z, B_x, B_y, B_z]$ to every point in space.
The time evolution of all six numbers is completely deterministic, but follows ...
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Does the azimuth angle matter for determining the electron density for atomic orbitals?
The only place in the expression for the wavefunction where the azimuth angle $\phi$ is used is in the equation for the spherical harmonics, and in the spherical harmonics there is only a single ...
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When spectrum of eigenvalues of Schrodinger equation is continuous or discrete? [duplicate]
There is a point which I do not understand about the Schrödinger equation. I will try to explain the issue.
Consider the Schrödinger equation:
$\hat H = \frac{ \hat p^2}{2m} + U(\hat x)$
and we are ...
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What does the finding the eigenvalue of a wavefunction physically mean?
In https://arxiv.org/abs/physics/0602145 (page 8), there is a passage which says that the discrete nature of the energy levels of an electron in a hydrogen atom comes from the fact that the solutions/...
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Is the total wavefunction always the product of the spin and spacetime dependent states?
Is the total wavefunction always the product of the spin state $ψ_s$ and the spacetime dependent $ψ(x,t)$ state?
I understand conceptually that if we have a homogenous magnetic field, then the ...
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Understanding the Pusey-Barrett-Rudolph (PBR) Paper and Possible Experiments to Test It
I was kindly pointed to the PBR paper by one of the other members here recently and have been trying to digest it. As one might imagine I have a wide range of questions but I'll try to keep things ...
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What happens in the square potential barrier during Klein Scattering in 1D graphene?
I have a question about Klein Scattering in a square potential barrier, $U$, incident on 1D graphene. I have managed to get these equations from continuity equations at $x=0$ and $x=L$ of the ...
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Wavelength of wavefunction graph [closed]
So my professor loves to make like 10 exam questions where we interpret some graphs of quantum wave functions. Now I really do not understand how he reads off the wavelength for instance in these ...
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Delta function in discontinuous derivative of a wavefunction
In variational principle problem; we need to find $\frac{d^2\psi}{dx^2}$ to find $\langle T \rangle$; if
\begin{align}
\psi = \begin{cases}
A \cos ( \pi x / a ) , & -a/2<x<a/2\\
0 ...
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What is the hydrogen atom wavefunction in cartesian coordinate? [closed]
The ground state wavefunction of the hydrogen atom is given in spherical coordinates in the form of this:
$$\Psi(r)= exp(-r)$$
where r is the radius from the center of the atom.
Suppose we would like ...
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Where no observer exists, does this mean the wavefunction never collapses?
In most places across the universe, there is no conceivably sentient candidate to act as an "observer" to this system.
Are we to believe that, in the emptiness of intergalactic space, or ...
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Meaning of eigenvalue of the position operator $\hat{x}$?
Apologies for asking a question which may be too basic. I understand at the conceptual level that a measurement collapses a wavefunction into a single spike, which will then evolve again immediately ...
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Is this explanation of the bra-ket notation correct?
I would be very grateful for feedback, particularly pointing any factual mistakes, in the below explanation of the bra-ket notation:
"Quantum mechanical expressions can be simplified using a bra-...
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