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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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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40 views

Calculating the probability of a given energy

Given a normalised wavefunction say $$\psi(x) = A\sin(n\pi x),$$ (where $A$ is a normalisation constant) I can calculate the probability of finding the particle being between a position $x$ and $x + ...
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1answer
48 views

How do I normalize this wavefunction? [on hold]

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 &\: ...
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4answers
148 views

Physical reason why the derivative of a wavefunction has to be continuous?

Question What is the physical reason (i.e. without any maths) that the derivative of a wavefunction (except with infinite potentials) has to be continuous? Other info I know that in the classical ...
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0answers
37 views

Photograph of Light as Wave and Particle [duplicate]

what is this? actually its the first photo of light as wave and a particle. The bottom "slice" of the image shows the particles, while the top image shows light as a wave. i have questions 1.how ...
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980 views

Is it guaranteed that wavefunction is well behaved everywhere?

I don't really know much about Quantum mechanics, but would like to know one simple fact. The state function $\Psi(r, t)$ whose magnitude gives the probability density of the position of the particle ...
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2answers
88 views

Position space wave function of an electron

In Wikipedia I find the wave function of a free particle to be $$ \Psi(\vec{r},t) = A\,e^{i(\vec{k}\vec{r}-\omega t)}$$ This is is a plane wave moving in the direction of $\vec{k}$ with speed (phase ...
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2answers
113 views

Why does the magnitude squared of the wave function give us the probability density? [duplicate]

My question doesn't go much beyond the title: Why does $$\left | \psi \left ( x,t \right ) \right |^{2}$$ give us the probability density of something appearing at a certain location? I understand ...
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2answers
109 views

Do bras and kets have dimensions?

I'm trying to understand more intuitively what bras and kets are, but some aspects of them remain a mystery to me. We usually think of $\psi (x)$ as having dimension of $[1/\sqrt{L}]$ so that ...
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0answers
21 views

Plane wave conditions

Which conditions have to be fulfilled in order to approximate a light beam by a plane wave (i.e. $\phi(x)\approx \phi(0)e^{ikx}$)? I am looking for both mathematical and experimental conditions. At ...
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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
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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225 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
45 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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1answer
301 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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255 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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36 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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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
49 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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2answers
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
299 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
94 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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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
147 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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53 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
134 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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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 ...
2
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3answers
377 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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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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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
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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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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
117 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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2answers
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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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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
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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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1answer
67 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
351 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
69 views

Normalizing 3-Dimensional Wave Function [closed]

How do you normalize a wave function in three dimensions with spherical coordinates?
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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
42 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
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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
54 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
84 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
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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
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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 ...