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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How to find $\langle x^2 \rangle$ of a wavefunction $\psi(x,t)$ [closed]

I know how to find $\langle x \rangle$ of such a function, but I'm not sure of how to find the variance or $\langle x^2 \rangle$ of this continuous function. Any help would be greatly appreciated. ...
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Definition of linear response kernel in terms of wavefunctions (Parr/Yang)

I'm trying to understand the derivation of the linear response kernel in Parr/Yang's "Density-functional theory of atoms and molecules". First some background information: We look at a system of $N$ ...
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45 views

Barycenter and relative coordinates for schroedinger equation of the hydrogen atom

Heyho, i just realized i am not sure how one gets from: $\Big(-\frac{\hbar^2}{2m_e} \Delta_{r_e} - \frac{\hbar^2}{2M_P} \Delta_{r_p} +V(r) \Big)\Psi(r_e,r_p) = E \Psi(r_e,r_p)$ to: ...
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time as consequence of hadronics [on hold]

it has occurred to me that time is solely consequence of non-electric fields, with latest work being reading about «anapole» cite: Simple theory may explain dark matter due to ...
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358 views

Bound states of the $V(x)=\pm \delta'^{(n)}(x)$ potential?

The $\delta(x)$ Dirac delta is not the only "point-supported" potential that we can integrate; in principle all their derivatives $\delta', \delta'', ...$ exist also, do they? If yes, can we look for ...
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1answer
32 views

Fourier expansion and transform - what about the phase of the waves that i am adding?

Say we have a wave on the surface of the water and we want to describe it as a sum of other waves. So we use Fourier expansion to add waves of different wavelengths. For simplicity, say we have to ...
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56 views
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537 views

Density of classical states in quantum theory

Let's first treat electrons as classical objects. I can evaluate the classical energy of each state in a configurational space (3N real numbers and, say, spins) using just Coulomb's law. Then I ...
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479 views

Schroedinger equation for hydrogen atom

I have got a problem understanding the meaning of the Laplace operator in the Schrödinger equation for the hydrogen atom. $$\Big(-\frac{\hbar^2}{2m_e} \Delta_{r_e} - \frac{\hbar^2}{2M_P} \Delta_{r_p} ...
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287 views

Quantum Mechanics in Electric Field

I am working on a problem which looks like this. Consider a charged particle with charge $q$ trapped in a box of length $L$ with finite constant potential $ V_0 $ on both ends. A constant (static) ...
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1answer
110 views

What does a light wave look like (3d model)

What does a light wave look like? The only models I can seem to find online are 2D waves, they just look like sin() graphs. I have seen the models of the two components of "light waves" (electric ...
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1answer
50 views

Probablity Wave and Wavefunction [closed]

Are wave function and probability wave same? Well I am a bit confused about wavefunctions and probability waves. I read in Fabric of the Cosmos by Brian Greene that they are same. Please help me and ...
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33 views

How can we construct wavefunction using given density matrix? [closed]

I have recently learnt that for isolated systems, density matrix and the wavefunction have same information content. Given a density matrix for an isolated system, is it possible to reconstruct the ...
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244 views

Degeneracy in One Dimension

I'm reading this wikipedia article and I'm trying to understand the proof under "Degeneracy in One Dimension". Here's what it says: Considering a one-dimensional quantum system in a potential ...
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4answers
4k 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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4answers
103 views

Physical intuition behind negative values for wave function?

So a positive and a positive wave function create a bonding orbital where the probability of finding an electron is summed while a positive and a negative create an anti-bonding orbital with a lower ...
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46 views

The propagator method versus Schrodinger time dependent equation [closed]

What advantage does the the propagator, $K(x,t; x',t')$, method has over the solution of Schrodinger time dependent equation (STDE) for example in harmonic ocillator problems? I don't see any. See ...
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1answer
1k views

Must the derivative of the wave function at infinity be zero?

I came across a problem in Griffiths where the derivative of the wave function (with respect to position in one dimension) evaluated at $\pm\infty$ is zero. Why is this? Is it true for any function ...
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1answer
70 views

Is the photon's wave function the same as an electromagnetic wave(light)? [duplicate]

The first that i have been taught in Quantum Mechanics is the photoelectric phenomenon. Without analyzing it, it concludes that when we shine light at the circuit(roughly speaking), the work required ...
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58 views

Do quantum wave functions curve spacetime before they are measured

Do wave functions cause spacetime curvature before they are measured, or would curvature only happen upon measurement? I guess the question becomes, do quantum wavefunctions carry energy while they ...
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158 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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1answer
173 views

Which position and momentum distributions arise from some wave function?

Consider a particle in one dimension with wave function $\psi(x)$. The probability density function describing how likely it is to find it in a given position is given by ...
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1answer
35 views

Probability and double slit

if a beam of identical particles at random distances from each other (or exactly 1/2 lambda between each other) travelling with the same v towards a double sllit do not interfere with each others wave ...
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Coupled quantum harmonic oscillator

Given the following Hamiltonian for two identical linear oscillators with spring constant $k$ and interaction potential $\alpha x_1x_2$; I was asked to find the expectation value $\langle ...
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1answer
74 views

Width of a 1 dimensional box with same ground state energy as hydrogen atom [closed]

I am trying to find the width $L$ of a one-dimensional box for which the ground state energy of an electron in the box equals the absolute value of the ground state of a hydrogen atom. No ...
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Why is $ \psi = A \cos(kx) $ not an acceptable wave function for a particle in a box?

Why is $ \psi = A \cos(kx) $ not an acceptable wave function for a particle in a box with rigid walls at $x=0$ and $x=L$ where $$ k = \frac {(2mE)^{1/2}} {\hbar} \, ?$$ I had plugged the wave ...
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67 views

How can a solution of the time-independent Schrödinger equation evolve in space?

I understand that if the Hamiltonian does not depend on the time, the Schrödinger Equation becomes separable, so you get $$ H \psi(x) = E \psi(x) $$ and $$ \Psi(x,t) = ...
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Potential energy function for high energy continuum?

For the hydrogen atom the quantised energy levels are: $$E_n = \frac{- 13.6 eV}{n^2}\quad\text{with}\quad n = 1,2,3...$$ One peculiar property of this quantisation is that for large $n$ the energy ...
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724 views

Normalization of Momentum Eigenfunctions: the number of particles

After finding the eigenfunctions $u_p(x)=Ce^{ipx/\hbar}$ of the momentum operator just like in this UCSD lecture notes, one seeks to normalize them, so one first tries: ...
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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 ...
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332 views

Confusion about 1-forms as introduced in “Gravitation” (Kip S. Thorne,…)

In the book Gravitation in chapter 2, paragraph 5, they introduce the concept of 1-forms by thinking about the momentum 4-vector differently. They first introduce the de Broglie 1-form as follows (I ...
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1answer
120 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 ...
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How to predict bound states in a 1 D triangular well?

Assume we have a (single) particle in a potential well of the following shape: For $x \leq 0$, $V = \infty$ (Region I) For $x \geq L$, $V = 0$ (Region III) For the interval $x > 0$ to $x < ...
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82 views

Schrodinger's equation with negative sign

In time dependent Schrodinger's equation as given in Schrodinger's lecture (Four Lectures on Wave mechanics, Blackie & Son, 1949, pg22) he arrives at $$\nabla^2\psi-\frac{4 \pi m ...
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What is probability current in quantum mechanics?

What is probability current in quantum mechanics? Why define such a thing? I mean the meaning of probability current. I know the formula for it but I just don't get the idea of a flow of probability ...
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1answer
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Normalizing a wave function in a mixed well

So I got this potential and want to solve for the even wavefunctions http://imgur.com/GKAy4nD Since it's symmetric around the origin I need only to look at the interval [0,b] and solve for the ...
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288 views

What do “ℜe” and “A*” mean?

What do "$\mathfrak{Re}$" and "A*" mean in the following equation (taken from James Binney and David Skinner's QM lecture notes, equation 1.12), \begin{align} p(S\text{ or ...
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1answer
49 views

Why do the two amplitudes need to match together through the region between the boxes?

This is an excerpt from Feynman's lectures 3; Suppose we think of the situation in Fig. 7–3, which has two boxes held at the constant potentials $ϕ_1$ and $ϕ_2$ and a region in between where ...
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411 views

Why does the wave function have to be continuous? [duplicate]

When solving one dimensional problems in quantum mechanics it is often assumed that the first derivative of the wave function is continuous. What justifies this assumption?
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Why can the probability function for a particle in an infinite square well be larger than 1?

For a particle in a one dimensional infinite potential well of width $L$ the probability function is: $$P_n(x)=\left(\frac{2}{L}\right)\sin^2\left(\frac{n\pi x}{L}\right)$$ for $0\leq x\leq L$. The ...
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265 views

Electron as a standing wave and its stability

1. When it was an era of classical mechanics we used to believe in the Bohr's atomic model. It interpreted electrons as particles (although I couldn't understand how come Bohr who interpreted ...
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429 views

Double slit experiment observation

In the double-slit experiment, if you shoot particles through the slits one by one and observe which slit they travel through, is there still an interference pattern on the screen behind the slits? If ...
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120 views

Wave Function concept

What do we mean when we say wave function of electron? Does it mean wave nature of electrons? I am really confused.Without clearing this confusion i cannot proceed to molecular orbital theory.I am ...
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Isn't the 'slit' in a double-slit experiment also a wave?

I'm new to QM so excuse my naivety. I was watching an online MIT QM course that described the double-slit experiment (with electrons) when it occurred to me that I have a question. In the video, the ...
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2answers
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Where does the factor of $x$ come from in this formula for expectation value?

Given the normalised ground-state wave-function: $$\Psi(x, t)=\begin{cases} \sqrt\frac{2}{d}\cos(\frac{\pi x}{d})e^\frac{-i\hbar\pi^2t}{2md^2} & \ \lvert x\rvert<\frac{d}{2}, \\ 0 & ...
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Cancelling waves and preservation of energy

In quantum physics, a particle is "defined" by a wavefunction. If you would take 2 particles with the same wavefunction, and negate one of them. They would cancel each other other out. Take for ...
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Solutions to time-independent Schrödinger's equation with symmetrical (even) potential [duplicate]

A problem from Griffith's Introduction to Quantum Mechanics asks to prove the following: Given a symmetric potential $V(x)$ $(=V(-x))$, the solutions to the time-independent Schrödinger's equation ...
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What state the wave function collapses into after an inaccurate measurement?

I'm watching MIT online lectures Quantum Physics I (roughly from one hour mark in the video). The lecturer explains wave functions that describe "Stationary States" that consist of a single energy ...
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The definition of the vacuum state of quantum field by path-integral

In the review Entanglement entropy of black holes by Sergey Solodukhin (arXiv:1104.3712, equation 13), I see a definition of vacuum state of quantum field by path integral over half of the total ...
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Wave packets and half-width at half-maximum

Suppose we have a Gaussian wave function and amplitude distribution function $$\psi(x) = (\frac{2}{\pi a^{2}})^{1/4}e^{-x^{2}/a^{2}}e^{ik_{0}x}, \qquad \phi(k) = (\frac{a^{2}}{2\pi})^{1/4}e^{-a^{2} ...