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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Proving spherical harmonic wave equation satisfies differential wave equation in spherical coordinates

I am just wondering how can you show that a spherical wave equation satisfies differential wave equation in spherical coordinates. I always see example at the book referring to planar waves, but can't ...
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39 views

Why is the full eigen function is product of eigen functions and not addition?

For example suppose there is a two electron system. Why is the full eigen function product of the spatial eigen function and spin wave function for the two electron system?
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34 views

Probability to be in a particular state

If I have a wavefunction $\psi = \sum_{n=0}^{\infty} a_n e^{i \phi_n} | n \rangle$ and $(|n \rangle)$ is a set of orthonormal functions. Is it correct that the probability to be in a state $|k\rangle ...
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310 views

Am I missing a trick to solving this differential equation?

I was playing around with a 3-D potential $V$ such that $V_{(r)} = 0$ for $r<a$, and $V_{(r)} = V_0$ otherwise. By using the Schrödinger Equation, I showed that: ...
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137 views

What is the physical reason behind linearity of Schrodinger's equation?

What is the physical reason for Schrodinger equation to be linear? Though in physics many interactions or dynamics are found non linear.
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66 views

Different mathematical methods in quantum mechanics?

My understanding is that in quantum mechanics the wavefunction may be expressed as a function or as a ket vector (composed of many orthogonal ket vectors). I'm not too sure about the further ...
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35 views

Question about Hartle and Hawking's universal wavefunction?

My apologies in advance if this question is poorly worded or doesn't make any sense, however I have just finished reading into this theory and it seems as though Hawkings No Boundary Universe is ...
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3answers
58 views

Koopmann von Neumann (KvN) Theory

I was just wondering does anyone have any informative sources apart from the obvious wikipedia articles regarding Koopmann von Neumann (KvN) theory? Or if its possible could someone explain the basic ...
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3answers
52 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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104 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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52 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
80 views

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

In the following research paper (link provided) , I am not able to figure out how do we get the equation (7) . Please help me out. Also , please recommend the necessary pre requisite text to ...
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30 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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41 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} - ...
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1answer
42 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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61 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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20 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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94 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) = ...
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286 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 ...
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1answer
105 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
56 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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82 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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61 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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69 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
234 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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461 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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29 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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42 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
59 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 ...
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48 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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76 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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44 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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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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42 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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125 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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53 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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118 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: ...
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1answer
46 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
37 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
117 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 ...
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42 views

Noncanonical commutation relation and noncanonical wave mechanics [closed]

Consider noncanonical operators $\hat{x}_1,\hat{x}_2,\hat{p}_1,\hat{p}_2$ satisying the following condition in the $q_1,q_2$ - basis ($\psi=\langle q_1,q_2|\Psi\rangle$)(similar to wave mechanics): ...
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45 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 ...
2
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2answers
77 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
53 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 ...
3
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1answer
39 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
111 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
642 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 ...
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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 ...
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61 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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60 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 ...