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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9 views

The difference between $R(r)$ vs $r$ graph for $4s$ and $5p$ orbital

Both orbitals have equal number of radial nodes (number of radial nodes = $n-l-1=3$). So the curve cuts the $x$-axis in 3 points. If it was $\psi^2$ vs $r$, then the curve would touch the $x$-axis at ...
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73 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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2answers
275 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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0answers
59 views

How do I calculate momentum for a particle in a box, using the momentum quantum operator? [on hold]

For a particle in a one dimensional box with $U(x) = 0$ between $x = 0$ and $x = L$ (infinite Potential well) the momentum for $n = 1,2,3,...$ is given by: $$p_n = \frac{nh}{2 L}$$ The wave ...
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44 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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2answers
89 views

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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3answers
232 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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3answers
108 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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27 views

Electron wave function seen in Quantum Cascade Laser?

http://sciencequestionswithsurprisinganswers.org/images/qcllevels.gif How did they observe and take a picture of the electron wave function without collapsing it? Does this prove that the wave ...
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2answers
69 views

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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4answers
139 views

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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20 views

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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0answers
28 views

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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35 views

C60 orbital calculation [migrated]

I am currently trying to reproduce the results published by Hands et al.1 using MALTAB. They calculated the bases of the C60 wave functions of HOMO, LUMO and LUMO+1. Now I have written these functions ...
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1answer
65 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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2answers
107 views

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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32 views

Transfer function of a space varying wave equation

$$\frac{\partial ^2 \psi}{\partial x^2}-\mu \epsilon \frac{\partial ^2 \psi}{\partial t^2}-\mu \sigma \frac{\partial \psi}{\partial t}=0$$ Is the wave electromagnetic wave equation in lossy, source ...
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1answer
50 views

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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1answer
38 views

$\sqrt{\frac{\omega ^2}{c^2}-k_z^2}$ in cylindrical harmonics

The radial component of the solution of the wave equation in cylindrical coordinates is $$J_\nu \bigg(\rho\sqrt{\frac{\omega ^2}{c^2}-k_z^2}\,\,\bigg).$$ But I always thought that $\frac \omega c$ ...
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1answer
47 views

Plane wave expansion of cylindrical functions:Summation of the Hankel functions

I understand that; in cylindrical coordinates, the basic solutions of the Helmholtz equation are of the form Hankel function of integer order times a complex exponential term ...
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3answers
210 views

Constructing solutions to the time-dependent Schrödinger's equation

The following question is from David Griffiths' Introduction to Quantum Mechanics: Problem 2.13 A particle in the harmonic oscillator potential starts out in the state $$\Psi(x,0) = A[3 ...
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5answers
114 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 ...
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2answers
53 views

Does a free electron, one that's not either in an atom or a wire, have an associated wave-function?

Would a free electron, one that's not either in an atom or moving through a wire, but moving through empty space on its own, have an associated wave-function? Or, is an electron described as a ...
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1answer
60 views

Solution of the Radial Part of the Schroedinger Equation [closed]

The general Schroedinger Equation is: $$\left[-\frac{\hbar^2}{2m}\triangle +V(r,\vartheta,\varphi)\right]\psi_{nlm}=E\psi_{nlm}$$ When considering free waves, i.e. $V(r,\vartheta,\varphi)=0$ and a ...
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50 views

Property of the wave functions of a free particle

How can I show that the following holds? $$\langle nlm\mid \partial_z^2\mid nlm\rangle=-\int_0^{4\pi}d\Omega\int_0^{\infty}drr^2\left|\partial_z\psi_{nlm}\right|^2$$ The wave functions of a free ...
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2answers
98 views

How do phase carries structural information about the function? [closed]

Suppose you are on a railway platform and you hear the sound of train coming towards you. Now, Using Fourier transformation we can convert the time domain function (here take sound as a function) ...
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50 views

For an event that can occur in many ways, why is the wavefunction of the event the sum of wavevfunction for each way separately?

The wavefunction of identical particles is given as: $$\psi_{1,2} (x_1,x_2) = \psi_1(x_1)\psi_2(x_2) + \psi_2(x_1)\psi_1(x_2)$$ . Why is it so? Why is it the sum of the two states? What is the ...
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1answer
100 views

How to visualize a Schrödinger cat state?

I recently read about Schrödinger cat states (SCS), which are basically a superposition of two coherent states $|\alpha\rangle$ with opposite phases, that is, $$ |cat\rangle = |\alpha\rangle \pm ...
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1answer
43 views

Analytical non-separable solution for schrodinger equation

I am an undergraduate with the background of a first course in Quantum Mechanics. I want to find out if there exist non-unique solutions to Schrodinger equation. So I have to find potentials ...
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1answer
87 views

What is the difference between real orbital & complex orbital?

While reading Atomic orbitals, I came before these two terms. The 'real orbital' is given here: Real orbitals An atom that is embedded in a crystalline solid feels multiple preferred axes, ...
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70 views

Where do these two equalities for the expectation value come from precisely? Doesn't $\Psi^* x \Psi = x |\Psi|^2$?

Where do these two equalities for the expectation value come from precisely? : $$\begin{align} \langle x\rangle &= \int_{-\infty} ^\infty \Psi^* x \Psi\,\mathrm{d}x \\ \langle x^2\rangle &= ...
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1answer
60 views

The Tunnelling Man [closed]

What's the probability that I will tunnel through a solid wall? By "tunnel" I mean, the probability of finding me on the other side of the wall. Assumptions Wall thickness = $d$ Clearly state any ...
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1answer
61 views

Finding the wave function of a quantum harmonic oscillator [duplicate]

How can I find the wave function of a quantum harmonic oscillator? If I measure its energy several times, my measurements will change the state of a system. All I know are the possible states, given ...
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2answers
81 views

Why is probability of finding the electron at a certain point when one of the slits is closed $|\Psi|^2 $ & not $|\Psi|^2 dx$?

Let in a given physical condition, the wave-function to a particle be assigned as $|\Psi (x_i,0,0,t)|^2 dx$. Now, at the double-slit experiment , the probability of finding the particle at any $x$ ...
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40 views

Particle in a box - speed probability distribution

Consider a particle in a box with infinite barriers. By solving the Schrödinger we can find the probability of finding the particle at some points in the box. How can we find the probability of ...
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3answers
85 views

How to measure the wave-function experimentally?

Do experimental physicists really measure the wave function of a system? How do they do it? Do they make many identically-prepared systems and measure the position of the particle(s) over and over ...
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2answers
100 views

What is the meaning of integrating over the state space?

If $\lvert\psi\rangle$ denotes the state space corresponding to a qubit, then what is the meaning of the $$\int d\psi$$ where the integral is over whole state space of a qubit? How do I evaluate it? ...
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3answers
65 views

Probability density for wavefunction given as infinite superposition of eigenstates

How do we find the probability density as a function of (x,t), if the wavefunction is expressed as an infinite superposition of eigenstates? When the wavefunction is expressed as a superpostion of ...
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1answer
63 views

Probability density for momentum in Quantum Mechanics

In a book i found the following equations: $$ \phi(k)=\frac{1}{\sqrt{2\pi}} \int_{-\infty}^\infty \Psi(x,0)e^{-ikx}dx $$ and $$ \Psi(x,t)=\frac{1}{\sqrt{2\pi}} \int_{-\infty}^\infty ...
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1answer
85 views

Problem with momentum values in a QM problem

I have the following equation of $Ψ$ around a ring (the particle is bound to move only on the ring): To visualize the state(it dies before L/2 if L=2πR): We can see from the first picture that ...
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1answer
124 views

Why “textbook examples” of solutions to Schrodinger equation only deal with electrons?

Whenever studying first courses of quantum mechanics, the Schrodinger eqaution is always illustrated by an electron in some kind of a potential, and the solution (wavefunction) represents probability. ...
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1answer
93 views

Fiber bundle understanding of the wavefunction

Usually people say that given a wavefunction $\Psi$ although $|\Psi(\cdot, t)|^2$ is the probability density for the position random variable at time $t$, the wavefunction $\Psi$ itself has no ...
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130 views

Time evolution of a wavepacket

I do not understand why if $H\psi = E\psi$, then the time-evolution of the wavefunction is given by $e^{-iEt/h}\psi(x)$.
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28 views

Molecular orbital theory

What I have learnt : When two waves overlap in phase, the resultant wave formed had a greater amplitude than that of the two interfering waves. When they overlap out of phase then the resultant ...
3
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1answer
113 views

What is the purpose of the imaginary portion of the wave function?

I recently watched this video. I'm trying to learn about the origin of the wave function and therefore understand its use in the Schrödinger Equation. However at the end of the video I understood up ...
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1answer
34 views

systems of particles that are not symmetric or anti-symmetric; Helium 4

Suppose I have an electron and a proton, and that the electron is in the spin-up state, and that the proton is in the spin-down state. The particles are distinguishable, so I should just be able to ...
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1answer
27 views

Applying operators to the wave function, getting the physical units

Reading the wikipedia entry about operators, in particular the table at the end listing all operators, I have several questions regarding an $N$-particle system or statements that I wonder whether ...
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1answer
54 views

Mach-Zehnder interferometry wave functions

Consider the set up below: I have read that in the apparatus the wavefunction is given by: $$|\psi \rangle=e^{i\theta}|c \rangle +i |b \rangle$$ where $\theta$ is the phase added by the phase ...
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1answer
50 views

Time dependent solution to infinite well

A particle of mass $m$ is confined within an infinite, one-dimensional potential well, $U(x)$, of width $a$. $$ U\left(x\right) = \left\{ \begin{array}{lr} \infty &\: x \leq ...
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1answer
59 views

How do I normalize this wavefunction? [closed]

I need to find the normalisation constant $A$ for the wave function: $$ \psi\left(x\right) = \left\{ \begin{array}{lr} A &\: \frac{-a}{4} \leq x \leq \frac{a}{4}\\ 0 &\: ...