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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508 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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3answers
224 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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2answers
43 views

Potential step and exponential decay?

Let us say we have a wave going from a region ($x<0$) where the potential is $U_1$ to a region ($x>0$) where the potential is $U_2$. The wave function in the second region takes the form: ...
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300 views

Integers, Energy levels, and wavenumbers for a particle in a 2D box

(This question is not about coding) I have built a little code in Python that allows the user to plot the energy vs the wave number of particle in a 2D box, depending on what values for the integers ...
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254 views

How to guarantee square integrable solutions to time-independent Schrödinger's equation?

Given the time-independent Schrödinger’s equation in one dimension $$H\psi = E\psi$$ what restrictions can we place on V(x) (inside the hamiltonian) and E to guarantee that the solutions won't have ...
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24 views

How can we calculate the spherical wave vectors L,M,N [on hold]

if we have a vector wave function in spherical coordinates ae^ikz. then how can we calculate its spherical wave vectors M,Nand L
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1answer
33 views

Finding the average energy from the superposition of state?

If I have two energy eigenstates $\psi_1(x)$ and $\psi_2(x)$ (corresponding to energy $E_1$ and $E_2$ respectively) and we prepare a particle in the superposition of both such that it is described by ...
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1answer
150 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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44 views

Quantum Physics - Step Potential? Don't understand it and how it relates to debroglie wavelength

Ok so I posted a question in the wrong format so it got closed, I hope this one is formatted better. I have a revision question that gives me the total energy of the electron, it then states that the ...
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1answer
48 views

Boundary conditions of the radial Schrodinger equation

Consider the radial differential equation $$\bigg( - \frac{d^2}{dr^2} + \frac{(\ell+\frac{d-3}{2})(\ell+\frac{d-1}{2})}{r^2} + V(r) + m^2 \bigg) \phi_\ell (r) = \lambda\ \phi_\ell (r),$$ which I've ...
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98 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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3answers
298 views

No well-defined frequency for a wave packet?

There are similar questions to mine on this site, but not quite what I am asking (I think). The de Broglie relations for energy and momentum $$ \lambda = \frac{h}{p}, \\ \nu = E/h .$$ equate a ...
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3answers
92 views

What's the correct link between Dirac notation and wave mechanics integrals?

In wave mechanics when we compute the expectation value of energy we write the following $$\left<\hat{H}\right>=\int_{-\infty}^\infty\mathrm{d}x\ ...
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1answer
46 views

Quantum Physics - What is the probability of it being in specific state (Stuck on question) [closed]

The normalised wavefunction for an electron in an infinite 1D potential well of length 65 pm can be written: $$\psi=(0.038 \psi_{n=1})+(-0.227\ i \psi_{n=10})+(g \psi_{n=5}).$$ If the state is ...
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1answer
36 views

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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1answer
146 views

Difference between expectation values of $L^2$, $L_z$ and measuring $L^2$, $L_z$

I was given with this hydrogen radial wavefunction $$ R_{21} =\left(\sqrt{\frac{1}{3}}Y^0_1 + \sqrt{\frac{2}{3}}Y^1_1\right) $$ and was asked to find a) What are the expectation values of the ...
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1answer
51 views

Orbital angular momentum of electrons

In a QM class, to study the hydrogen atom, we started by defining the Hamiltonian $H$ for a central potential, then made an orbital angular momentum operator appear as part of $H$, then down the line ...
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1answer
107 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
133 views

Eigenvalues of the radial Schrödinger equation on a finite integration interval

There are numerous ways to estimate the eigenvalues of a radial Schrödinger equation, see http://arxiv.org/abs/math-ph/0703040 as an example. Anyhow, the formulas only cover the Schrödinger equations ...
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11 views

Periodic Boundary Conditions in 2D Box [duplicate]

In a 2D box with both dimensions of $L$, the electron can move freely within this large box. Use periodic boundary condition, and find the wavefunctions and corresponding energies in this 2D box. I'm ...
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3answers
373 views

Who is doing the normalization of wave function in the time evolution of wave function?

In the Schrodinger equation, at any given time $t$ we should jointly add another sub equation, like $$||\psi_t(x)|| = 1$$ where $\psi_t(x) = \Psi(x,t)$, and then try to solve the two equations ...
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1answer
23 views

Scintillation from wave function

Suppose we have a system with a (non-relativistic) electron whose state is described by a time-dependent wave function $\psi(x,t)$. Then I think it's correct to say that if we introduce a phosphor ...
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1answer
34 views

Question about group velocity and travelling waves

I'm trying to learn some basic quantum mechanics and I have a question related to group velocity of a travelling wave. I know there are already a few questions related to group velocity, but I ...
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1answer
2k views

3D Quantum harmonic oscillator

For an isotropic 3D QHO in a potential $$V(x,y,z)={1\over 2}m\omega^2(x^2+y^2+z^2).$$ I can see by independence of the potential in the $x,y,z$ coordinates that the solution to the Schrodinger ...
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3answers
146 views

What is the meaning of “ Ψ is not a measurable quantity in itself”?

I want to know that why the wavefunction Ψ as a complex quantity (i.e $A+iB$ form) in quantum mechanics and somewhere I have studied that Ψ is not a measurable quantity in itself that's why we ...
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1answer
115 views

Questions about the formalism of Quantum Mechanics

I have to do a presentation on this. I'm not expected to do something really detailed, but I'm not understanding the mathematical formalism. I would like to receive general answers to these questions: ...
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87 views

What state does the particle in a box occupy?

My textbook derives the equations for the different energy states $E_n$ of the particle in a box. But my professor in class said this example was a good one because it spoke about the "superposition ...
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1answer
26 views

Is the Singlet state for Helium with 2 electrons symmetric rather than anti-symmetric as is meant to be for fermions?

I'm looking at two-electron Helium atoms where one electron is in the ground state (due to if it were in other states, it's de-excitation would simply lead to the ionization of the electron). The ...
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3answers
460 views

The meaning of the phase in the wave function

I have just started studying QM and I got into some trouble understanding something: Let's say there is a wave function of a particle in a 1D box ($0\leq x\leq a$): $$\psi(x,t=0) = ...
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2answers
1k views

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
58 views

Why is the position space free particle wavefunction a function of momentum?

This is one of those little things that has always confused me. If someone said to you "in quantum mechanics, the eigenfunctions of a free particle are $\exp(ipx/\hbar)$" how would you know that ...
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1answer
350 views

How to find the time evolution for two-component spinor? [closed]

I would like to find the time evolution for the given Hamiltonian, the initial state of the system we choose two spinor wavefunction $\psi_{+}(t=0)$ and $\psi_{-}(t=0)$ as given below: The effective ...
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2answers
65 views

Normalizing 3-Dimensional Wave Function [closed]

How do you normalize a wave function in three dimensions with spherical coordinates?
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2answers
174 views

Calculation of the $\langle H \rangle$ for a particle in a box

I am working through a problem in which a particle is in an infinite potential well of length $L$ at $t=0$ before the spontaneous change of the box being expanded to length $2L$. I have calculated the ...
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0answers
38 views

Free particle scattering in 2D using polar coordinates

The free particle hamiltonian commutes with the angular momentum operator L and Lz, so we can use a spherical wave basis instead of the regular plane-wave basis |k>, using spherical Bessel function ...
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1answer
80 views

Understanding the behavior of light/photons inside a Laser

I am trying to establish a model inside my head of how light behaves but find it hard with all the seemingly contradicting information. For example, electrons inside a Laser are raised to a higher ...
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2answers
36 views

What the wave function looks of a particle in the infinite square well looks like after collapse for measurements of position and energy

Consider a particle in a the infinite square well from x=0 to x=L. At t=to, I make a measurement of position and get x=L/2. What is the resulting wave function at t=to? My understanding, from reading, ...
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1answer
53 views

Normalisation of a wavefunction [closed]

If the system if found in the state: $$\psi=\sqrt{\frac{1}{2\pi}}(\frac1{\sqrt3}e^{-i3\phi}+ce^{-i4\phi})$$ what value of $c$ normalizes the wavefunction? Clearly: $$\int_0^{2\pi}\psi^*\psi ...
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1answer
80 views

Probability of finding particle in infinite square well, displaced walls

Initially a quantum particle moves in a one-dimensional well ($x$-axis) from $-a$ to $ a$, $ V = \infty $ outside and $ V = 0 $ inside the well. So initially, the wave-function $$ \psi_0 = ...
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1answer
58 views

How to separate k into real and imaginary parts?

In $k^2 - \frac{\omega^2}{c_o^2} + (\tau_{\alpha} i \omega)^{\alpha} k^2 = 0$, $k$ is the wavenumber, $\omega$ is angular frequency, others are constants. How can I separate the wavenumber $k$ into ...
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1answer
38 views

Importance of bound states

While solving a potential well problem we get scattering states and bound states (if exist). Number of the bound states we get depends on the potential profile. What I want to ask is, what is the ...
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119 views

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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1answer
78 views

Quantum Mechanics Notation

Generally we have that $$|\psi\rangle=\int_{all space} \psi(\mathbf x)|\mathbf x\rangle d^3\mathbf x$$ and therefore $\psi(\mathbf x)=\langle\mathbf x|\psi\rangle$. When discussing the mutual ...
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2answers
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The probability of finding the electron in the H-atom

In the book Arthur Beiser - Concepts of modern physics [page 213] author separates the variables in the polar Schrödinger equation assuming: $$\psi_{nlm}=R(r)\Phi(\phi)\Theta(\theta)$$ then there a ...
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1answer
79 views

Has anyone published the procedure to generalize ladder operators for any potential in Schrodinger's equation?

I know that the ladder operator for the quantum harmonic oscillator \begin{align} H\psi_m = \left(\dfrac{p^2}{2m}+\dfrac{1}{2}m\omega^2x^2\right)\psi_m=E_m\psi_m \end{align} is \begin{align} A = ...
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320 views

Is normalization consistent with Schrodinger's Equation?

Schrodinger's Equation does not set a limit on the size of wave functions but to normalize a wave function a limit must be set. How is this consistent physically and mathematically with Schrodinger's ...
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Why position and momenta are fluctuating quantities?

In a coordinate basis we have $$\langle \Psi \mid \Psi \rangle = \int \prod_{i=1}^N d^3q_i |\Psi(\textbf{q}_1,\dots,\textbf{q}_N)|^2=1$$ This means that for any quantum state $\mid \Psi ...
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5answers
736 views

Quantum Wave Mechanics

I am studying QM-I these days. Now, I just think of the wave function as just a mathematical function that defines the state of the particle at an instant and from it you can extract various ...
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5answers
1k views

Hydrogen radial wave function infinity at $r=0$

When trying to solve the Schrödinger equation for hydrogen, one usually splits up the wave function into two parts: $$\psi(r,\phi,\theta)= R(r)Y_{l,m}(\phi,\theta).$$ I understand that the radial ...
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2answers
65 views

Particle in a one dimensional box conditions

Why does the wave function have to be $C^1(\mathbb{R})$ for a finite square well but not for an infinite square well? For an infinite square well with boundaries at $x=0$ and $x=L$, we have ...