# Tagged Questions

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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### Observer in the double slit experiment with photons

In the double slit experiment with photons, the interacting observer is an instrument, detector… If you replace the detector with a piece of metal with the same mass as the mass of the detector, the ...
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### Correlating two definitions of bound states in quantum mechanics

In Griffiths, he defines a bound state to be that stationary state for which the total energy E is such that $E<V(\pm\infty)$. Let $\psi(x)$ is a stationary state satisfying $E<V(\pm\infty)$ and ...
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### Wave function of particle and antiparticle

The wave functions of particle and antiparticle are related by complex conjugation and wavefunction Ψ must be complex for particle such as n, p. Is there way to prove this mathematically? Can we do ...
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### How to calculate probability of complex wave functions? [closed]

An election has an equation as such: $$Ψ(x) = e^{iαx^2}.$$ How am I supposed to find the probability of finding the electron over a certain range? Is Fourier Transform involved in this?
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### Is there a way to prove that a bound state wavefunction can always be chosen real for an arbitrary potential in Quantum Mechanics?

As we can prove many things that always (at least in introductory quantum mechanical problems) apply using an arbitrary potential (like that $E>V_{\rm min}$ or else the solutions are non-...
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### Connection between Hamiltonian version of the least action principle and probability amplitude in the Schrödinger equation

If I'm not mistaken, Schrödinger was influenced to look at wave equations because of de Broglie's assertion about particles having a wavelength. He started with the Hamiltonian equation which is ...
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### Particle here at a given time, in another galaxy a second later… Really?

I read "The Quantum Universe (Cox & Forshaw)" that a particle can be measured at a given position at a given time, and in another galaxy one second later. The probability of such event may be ...
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### Three particles case, finding ground energy state

Here I came up with three particles in a box problem. (Assumption: Here I do not consider the interaction between particles and spin for simplicity.) What I want to do is express the ground state's ...
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### What is a linear polarized photon?

According to Dirac a 'linear' polarized photon is a superposition of left and right rotating photons. Here is a puzzling aspect of this superposition. There are dichroic materials which can absorb ...
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### Representing an ISW wavefunction graphically [closed]

I'm trying to decode this diagram given to us for an assignment. The description of the diagram is 'Consider a particle of mass m confined to a 1-dimensional square well, given graphically by the ...
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### Meaning of the Vector Wave Equation

So I thought I would try my luck here on physics stack exchange about an intuitive meaning of the Vector Wave Equation. I know there are a lot of resources out there that explain this equation, but ...
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### Calculating the energy of a particle using the Time Independent Schrodinger Equation [closed]

If we have a wave function $\Psi(x,t=0)$ which is a solution to the TISE for a zero potential in an infinite square well, would calculating the energy at $t = 0$ at a position be as easy as ...
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### Exchange principle in terms of states and coordinates?

I have seen the exchange principle written in two ways, one in terms of coordinates and the other in terms of states: If $\psi_{AB}(1,2)$ represents particle $A$ in state $1$ and particle $B$ in ...
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### How do we know that there is a wavefunction which collapse?

How do we know that there actually is a wavefunction in the first place which collapse. How do we know that there is a transition from some linear combination of the eigenfunctions to a single one? ...
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### Is the wave function of a particle re-created after a measurement stops?

Yeah, I haven't quite understood, or been told, what happens to, for example an electron and its wavefunction, when you stop to measure it. I mean, an electron has a wave function describing its ...
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### Significance of $i$ in the Schrödinger equation [duplicate]

There's an imaginary $i$ in the Schrödinger equation, which I guess is to define the position of the particle in a space-time involving a complex function. But what is the real physical significance ...
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### How can a probability distribution have wavelength (de Broglie wavelength)?

The wave function described by Schrodinger's equation is interpreted as describing the probability of a particle in at any point in space, i.e. a probability distribution. Since this distribution ...
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### 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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### The formal solution of the Schrodinger equation

Consider the Schrödinger equation (or some equation in Schrödinger form) written down as $$\tag 1 i \partial_{0} \Psi ~=~ \hat{H} \Psi .$$ Usually, one likes to write that it has a formal solution ...
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### 1D transmission lines wave equation solution

you may know that the solution of 1D wave equation by d’Alembert is F(x-ct)+F(x+ct) and my question is that like is this F(x-ct) at transmission lines only the equation of one forward going wave that ...
When deriving the expression for the first order correction to the state vector of the new hamiltonian( H = H0 + H' ) we assume that $|\psi$n1> = $\sum_{m \neq n}$ C$_m$(n) $|\psi ^0 _m>$ $... 0answers 53 views ### Wave function for step potential Given the step potential $$V(x)=\begin{cases} 0~~~~~~~~\text{if }~~x \leq 0 \\ V_0~~~~~~\text{if }~~x > 0 \end{cases}$$ Consider the case where$E < V_0$. In this region$x \leq 0$we have ... 4answers 2k views ### Why do electrons in an atom occupy only the stationary states? When we talk about the elementary problems in quantum mechanics like particle in a box, we first calculate the energy eigen-function. Then we say that the most general state is the linear combination ... 0answers 42 views ### Help normalising and taking the inverse Fourier transform of this wavefunction [closed] Normalising Consider the wavefunction $$\psi(x,0)=Ne^{-\frac{|x|}{\lambda}}.$$ In order to normalise this I take the integral, which due to the modulus on the$x$I evaluate just from zero to ... 2answers 68 views ### Quantum Mechanics: How to compute how fast must a function go to zero at infinity? [closed] We say that the wave function must go to zero at infinity faster than$1/x^{0.5}in order for it to be normalizable. What about other quantities like the probability current? What is the general rule ... 2answers 90 views ### Normalization of a wave function in quantum mechanics A more simple question, so I am watching a quantum mechanics lecture on potentials of free particles and am doing the general solution of schrodinger's stationary equation for a free particle when I ... 0answers 65 views ### Expanding a wavefunction [closed] I have a wave function that I have already normalised: $$\psi(x) = \sqrt{\frac{30}{a^{5}}}x(a-x)$$ but now I have been asked to expand it to get: $$\psi(x) = \sqrt{\frac{960}{\pi^{6}}}\sum_{k} \... 3answers 196 views ### On the completeness relation in Quantum Mechanics Why does$$ \sum_n \Phi^{\ast}_n(x)\Phi_n(r)=\delta(x−r) $$represents a completeness relation? Or, put differently, why does it imply completeness? Is there any way to see it intuitively? Maybe an ... 1answer 58 views ### Why is the reflection coefficient in quantum mechanical scattering defined this way? In Griffiths' "Introduction to Quantum Mechanics, second edition" section 2.5.2, p. 73, he states: For the delta-function potential, when considering the scattered states (with E > 0), we have ... 1answer 60 views ### Should state vectors be considered constant? By the principle of superposition, a state vector can be defined as$$\begin{align} \psi(x) &= c_1 \psi_1(x) + c_2 \psi_2(x) + \cdots + c_n \psi_n(x) \\ \lvert\psi\rangle &= \begin{pmatrix}c_1 ... 1answer 28 views ### How to tell when exponentials are real valued? (Barrier Potential) Wherek_1=\frac{\sqrt{2mE}}{\hbar}$and$\alpha=\frac{\sqrt{2m(V_0-E)}}{\hbar}$I'm quite confused as to why the exponentials in regions I and III are complex functions while in region II the ... 1answer 37 views ### Existence of representation of symmetry transformation There is a simple fact that we can change our point of view and that physical laws should remain the same, id est, outcomes of our experiments should be the same no matter from which frame of ... 0answers 24 views ### Perodic boundary conditions vs Dirichlet? I have been working through several examples recently involving particles in boxes (when finding the partition function of an ideal gas for example or looking at photon gases). I have seen two ... 0answers 44 views ### Aharonov-Bohm effect [closed] In the build up to Aharonov-Bohm effect, one has to represent the gauge covariant form of STIE. We need to consider two things; the vector potential A changes`under gauge transformation and as a ... 3answers 137 views ### What are the functions of these coefficients$c_1,c_2,c_3,c_4$in$ \psi_{sp^3}= c_1\psi_{2s}+ c_2\psi_{2p_{x}} + c_3\psi_{2p_y}+ c_4\psi_{2p_{z}}$? Hybridised orbitals are linear combinations of atomic orbitals of same or nearly-same energies. Atomic orbitals interfere constructively or destructively to give rise to a new orbital which is what we ... 2answers 96 views ### Difference between a wavevector and wavefunction I often see both terms used in textbooks, but I am not sure whether I understand the difference between them. Both describe the state of a system, however, they seem different in some ways. From what ... 1answer 59 views ### General expectation value I have a basic question related to finding expectation values of an operator$\hat{Q}$We know that the expectation of$\hat{Q}$(in the position space) is given by $$\langle Q \rangle=\int {\Psi^* ... 2answers 109 views ### Derivation of Schrodinger's wave equation To derive$$i \hbar \frac{\partial}{\partial t} \psi = H \psi,$$we start with$$i \hbar \frac{\partial}{\partial t} |\alpha \rangle = H| \alpha \rangle$$and then multiply by \langle x| on the ... 1answer 64 views ### Perturbation by electrical field in infinite potential well: difference in first energy corrections because of difference in the limits of the well In time independent perturbation theory we can calculate the first and second energy corrections resulted by a potential V in the Hamiltonian H=H_o + λV , , λ<<, by the expressions:$$ε_1 = ... 5answers 199 views ### Does measurement change the evolution of wave function? Basically any measurement is on wave function$|\psi\rangle$is done by operator$X$such that$X|\psi\rangle$results observable$x$with some probability. But what happens to$|\psi\rangle$? Does ... 5answers 667 views ### How does a Wavefunction collapse? I have been wondering and researching... How does a wavefunction collapse into one state?More specifically, what conditions cause a wavefunction for a quantum particle to collapse? Does this have to ... 1answer 46 views ### Probability of finding electron in a spherical shell In the book Arthur Beiser - Concepts of modern physics, probability of finding an electron in Hydrogen atom in the spherical shell between$r$and$r+dr$is given as P(r)dr = r^2|R(r)... 0answers 41 views ### Continuous spectra and quantum decoherence Suppose that some quantum wave function$\psi = \int a_i \,i\rangle \,\,di$where pseudo-spanning ket "vectors" of$\psi$,$i \rangle$, are continuous. (thus the use of integral.) By normalization,$...
I'm confused in finding the condition for minimum uncertainty, The author in the book I refer goes on saying that $|g\rangle=c|f\rangle$ is the condition for minimum uncertainity for some constant \$...