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.

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Bound states in 1D & 2D [duplicate]

Why does Mother Nature allow bound states in arbitrarily weak attractive potential in 2D but not in 3D? See, for example, this article, arXiv:math-ph/0208011.
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3answers
88 views

What does “coherent wave function of a macroscopic body” mean?

What is meant by the "coherent wave function of a macroscopic body"? I found this phrase in a paper on QM, but am unfamiliar with the terminology.
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1answer
152 views

What does the notation $\Psi_k/(\Psi_k,\Psi_k)^{1/2} $ mean?

I am currently reading the paper "Gravitation and quantum mechanics for macroscopic objects" by F. Karolyhazy (1966). In his paper, he uses certain notation that I haven't come across before (he also ...
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0answers
86 views

1-particle momentum eigenfunction in terms of field operator for real Klein-Gordon field

Suppose $\phi(x)$ is a real Klein-Gordon field, then the single-particle wave function $\psi(x)$ corresponding to a momentum $p$ is given by (QFT, Ryder) $$\psi_p(x)=\langle0|\phi(x)|p\rangle.$$ The ...
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1answer
153 views

Doubt in a certain equation of a research paper [closed]

In the given paper, I am stuck at equation (7). The equation that I am trying to solve for particle outside the well is : (1/g)*(g'') + (1/(r*g))*g' - (k_o)^2 = 0 where g = Radial wave function. r = ...
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1answer
71 views

Expected value $<\hat{x}>$ of: $\Phi(x,t)=Ne^{-a[(Mx^2/\hbar)+it]}$ is infinite, why?

The problem says: A particle of mass $M$ is described by the wave function: $$\Phi(x,t)=Ne^{-a[(Mx^2/\hbar)+it]}$$ where a is a positive constant. Asked to determine such things as the ...
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0answers
285 views

Complex Conjugate of Wave Function's Derivative

I am reading Griffiths QM textbook and I got confused by the following identity: How to prove from $$\frac{\partial \Psi}{\partial t} = \frac{i\hbar}{2m} \frac{\partial^2 \Psi}{\partial x^2} - \frac{...
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1answer
221 views

Eigenfunctions corresponding to degenerate spectra

It is well knwon that an eigenstate can be obtained by superposing wavepackets. In other words, if $\Psi({\bf x},t)$ is the solution of the time dependent Schroedinger equation for an initial ...
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1answer
88 views

Wavefunctions and Quark Confinement

While I have a decent knowledge of general relativity (and, of course, classical mechanics), I am quite a novice when it comes to quantum mechanics, so I apologize if this is a rather basic question. ...
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168 views

Relation between p+ip wave Superconductor and Moore-Read State

I am quite interested in the understanding of the relation between p_ip wave superconductor(SC) and the Moore-Read(MR) state. They share many similar properties, for example, p+ip SC has majorana as ...
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2answers
423 views

Determining the Wave Function From Initial Conditions

This is Problem 2.6 (b) in Griffiths, Intro to QM: A particle in an infinite square well has its initial wave function an even mixture of the first two stationary states: $\Psi(x,0) = A[\...
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445 views

Does a wavefunction interact with itself?

Considering the double slit experiment with a charged particle, after the particle passes through the slits, do the two portions of the wavefunctions feel the electromagnetic attraction of the other ...
3
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1answer
305 views

Why is $\omega = \sqrt{K/m}$ valid for a quantum oscillator?

I'm working in the 3rd edition of Modern Physics by Serway, Moses, and Moyer. In 6.6, it talks about a quantum oscillator. I don't fully understand how the definition of frequency works. Now, we ...
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1answer
2k views

Determine the normalisation constant of a piecewise wavefunction

I'm trying to find the normalisation constant $N$ for the following wavefunction: $$ \psi\left(x\right) = \left\{ \begin{array}{lr} N \left(x^2 - l^2\right)^2 &\: \left|x\right| \le l ...
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2answers
215 views

Is the mechanics of the wave function in the quantum mechanics deterministic?

Is possible a non-deterministic propagation of the wave function in the QM?
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1answer
99 views

Where does either Bohr or Heisenberg mention the idea of the wave function collapsing?

Could someone reference a paragraph written either by Heisenberg or Bohr where they mention the idea of the wave function collapsing?
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1answer
169 views

Spin-½ and beyond: Measuring spin components other than ± ħ / 2: How to formulate the probability function?

It is my understanding that in quantum mechanics (for 1/2 spin particles) the probability function that describes the direction of a particle's spin state is proportional to the overlap of the ...
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3answers
543 views

Interpretation of the wave function in quantum mechanics

I just started watching the coursera lectures on the basics of quantum mechanics and one of the first lectures were on deriving Schrodinger's equation and its interpretation it under Born's ...
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5answers
3k views

Differences between probability density and expectation value of position

The expression $\int | \Psi\left(x\right)|^2dx$ gives the probability of finding a particle at a given position. If wave function gives the probabilities of positions, why do we calculate "...
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1answer
43 views

Variable definition in wave function for scattering particle?

For the wave function of a scattered particle when finding the scattering aptitude we have: $$\psi(r)=Ae^{ik_0∙r}+\frac{2\mu}{\hbar^2} ∫G(r-r')V(r')\psi(r')d^3r'$$ I was wondering what the variables ...
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1answer
176 views

Symmetric eigenfunctions?

So a symmetric eigenfunction / wavefunction is defined as: $$P_{ij} ψ_a (r_1,r_2,…,r_i,…,r_j,…,r_N )=ψ_a(r_1,r_2,…,r_i,…,r_j,…,r_N )$$ But for it to be symmetric does this have to be true for all $ij$ ...
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1answer
83 views

Normalising a wave function in parts?

If we have the wave function $\psi_{100}(r,\theta,\phi)=R_{10}(r)Y_{00}(\theta,\phi)$ when we are normalising it we do the following: $$1=\int| \psi_{100}(r,\theta,\phi)|^2sin(\theta) r^2drd\theta d\...
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2answers
118 views

Observables in Quantum Mechanics

Studying on own quantum mechanics I came across: Preceeding text: A basic postulate of quantum mechanics tells us how to set up the operator corresponding to a given observable. Observables, $\...
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2answers
820 views

Differences between wave function and set of orthonormal wave functions?

I'm reading a QM book. It first says for wave function: "The state of a physical system (or particle) is completely specified by an entity associated with it called a wave function, Ψ , that in ...
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1answer
140 views

Wave packets and amplitude

If a wave packet is given by: My question is basically how do we choose the write $A(k)$ to fit the particle we are looking at, or does it not matter (as my matter as my textbook seems to imply) ...
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109 views

Mathematical derivation of interference pattern for electrons?

One of the most famous experiments in quantum mechanics in the context of wave-particle duality is certainly passing a beam of electrons through two slits, which results in an interference pattern ...
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1answer
258 views

(Level: Undergrad) Continuity Conditions on the Wavefunction and Initial Values

I know that a physically meaningful $\Psi$ needs to be continuous. However, recently I came across a problem in which they were considering a wavefunction for the infinite square well potential and ...
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2answers
255 views

What is the analogy of $|x\rangle$ in quantum field theory?

Let me start from path integral formulation in quantum mechanics and quantum field theory. In QM, we have $$ U(x_b,x_a;T) = \langle x_b | U(T) |x_a \rangle= \int \mathcal{D}q e^{iS} \tag{1} $$ $|...
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1answer
92 views

How can we “know” that system interacted with another system or environment in quantum mechanics/decoherence?

I might be raising measurement problem in quantum physics in different words, but I will ask the question. Quantum decoherence has been proposed by proponents as a theory that eliminates all weird ...
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4answers
10k views

Differences between wavefunction, probability and probability density?

I am trying to understand the differences between wavefunction, probability and probability density. There are different definitions on the internet. For example: http://inside.mines.edu/~fsarazin/...
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1answer
192 views

Adding versus multiplying identical photons' wavefunctions?

I am currently confused with understanding many identical photons' wavefunctions. I think that photon wavefunctions are supposed to be multiplied together to describe the total state of all bosons. ...
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1answer
78 views

Are all identical fermions in orthogonal states as opposed to different general states?

A professor told me that most physicists assume that all identical fermions are in completely orthogonal states. If that is true, then does that mean that that the total wave function is highly ...
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3answers
154 views

I am learning Quantum Mechanics and I have some questions about some basic concept [closed]

What does a "STATE" exactly mean in quantum mechanics? What is the equivalence of "STATE" in classical mechanics? If we have a wave function $\Psi$ , its absolute square $|\Psi|^2$ is the probability ...
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2answers
413 views

Finite Square Well Inside an Infinite Square Well

Ok here's a potential I invented and am trying to solve: $$ V(x) = \begin{cases} -V_0&0<x<b \\ 0&b<x<a \\ \infty&x>a \\ \end{cases}$$ and $V(-x) = V(x)$ (Even ...
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2answers
204 views

Logic of the 'imaginary wave function collapse' argument in Double Slit experiment

My question is in regards to the stance that the 'wave function collapse' is not an actual physical occurrence. That is, you are not, by observation, changing the particles position from a wave to a ...
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1answer
547 views

Sign of the wave function in orbital representation?

I have some fog in my head and a rather simple question for you: When the sign of the wave function is representated on orbitals, what is this sign? I mean is it the sign of the real part of the ...
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1answer
263 views

Finite potential well, parity of solutions

I'm working through some problems for a QM exam and I've realised I don't really understand the concept of parity of solutions. I'm looking at a simple finite potential well problem: $$V(x)=0, \quad |...
3
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1answer
300 views

Probability of measuring momentum [closed]

Suppose we have this wavefunction: $$ \psi = A \left( cos(kx) + cos (2kx) \right) $$ I have to find the possible results of measurement of momentum and their probabilities. Attempt For a momentum ...
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2answers
168 views

Representations in quantum mechanics [closed]

This might be a very simple question. I just want someone to point me the right direction to understand things like this: $$ \langle x|x'\rangle=\delta(x-x') \\ \psi(x)=\langle x|\psi\rangle \\ \...
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5answers
794 views

Is there any operator behind probability, in quantum mechanics?

In Quantum mechanics, the probability of finding a particle at position $x$ is given by $|\psi(x)|^2$, where $\psi$ is the wave function. Wonder what is the operator which gives this probability? Is ...
2
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2answers
299 views

Quick question on sketching wavefunction in well

Usually for an infinite well, the sketch for n=3 level is this: Now I think if one side of the potential barrier is higher, the particle will be more likely to spend time on the left side than the ...
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0answers
346 views

Ground State Functional and Vacuum-Vacuum Transition Amplitude

In Path Integral formalism, the vacuum-vacuum transition amplitude is defined to be (the functional integration is over all field configurations in the whole spacetime; $\Phi_{\vec{x}}(\tau)$ is the ...
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2answers
234 views

Stationary state of time-independent Schroedinger equation is always real valued function?

I am reflecting on the solution of the time-independent Schroedinger equation. My reasoning is that the stationary state of the time-independent Schroedinger equation must be a real valued function ...
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2answers
237 views

details for the double slit experiment

In the double slit experiment with electrons, are all electrons going through the slits? If the electron gun is directed between two slits, than it should hit the central part between the slits, isn't ...
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1answer
166 views

How does a unique electron probability distribution correspond to one wavefunction?

I'm reading the Wikipedia article on DFT, and it says that there is a one-to-one correspondence between the ground state particle density $$n_0(\vec{r}) = N \int \text{d}^3 r_2 \int \text{d}^3 r_3 \...
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1answer
486 views

How to determine the transmission coefficient of a gaussian wave packet scattering on an finite square well?

I am doing a scattering simulation of a Gaussian wave packet on a finite square well. I have solved numerically the Schroedinger equation and I know the values of the wave function after the ...
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4answers
859 views

Double slit experiment and single particles. Is the wave function just a mathematical model?

I really do want to apologize in advance, I know this question has been 'answered' before. I have this 'problem' of feeling negatively toward much of today's 'mystical' interpretations of physics, ...
2
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1answer
123 views

On use of Hamiltonians for Helium

The Hamiltonian of helium can be expressed as the sum of two hydrogen Hamiltonians and that of the Coulomb interaction of two electrons. $$\hat H = \hat H_1 + \hat H_2 + \hat H_{1,2}.$$ The wave ...
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2answers
4k views

Particle in a 1D Box with Symmetric potential: How find solutions?

I am working on a problem in which I shall find the normalised solution to the 1D particle in a box. Solving for the particle in an asymmetric potential is quite straight forward, but I run into ...
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1answer
129 views

Is it possible to find the hydrogen atom's radial wavefunctions?

Is there a way to actually find the equation of $R(r)$ without looking at a table with these equations already given? I'm given $n$, $\ell$, and $m$.