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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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: ...
-2
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0answers
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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2answers
253 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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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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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
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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0answers
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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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
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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2answers
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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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
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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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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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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0answers
37 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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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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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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0answers
46 views

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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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 ...
6
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1answer
328 views

What is a 'turning point' in WKB and why does it fail at that point?

What is meant by a classical turning point in quantum mechanics and why does the WKB approximation fail at that point?
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1answer
97 views

Is de Broglie matter wave a mass or a particle hypothesis?

I'm having difficulty understanding de Broglie matter wave hypothesis. It is a mass or a particle hypothesis? According to de Broglie a particle with mass $m$ moving at a constant speed has an ...
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1answer
57 views

How to calculate the expectation value of position vector?

$$\psi (\vec{x})=Ae^{-(1/4a^2)|\vec{x}-\vec{x}_0|^2}e^{i\vec{p}_0\cdot \vec{x}/\hbar}$$ The wave function is like this, then how is the expectation value of position vector (not position) calculated? ...
0
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1answer
42 views

How to solve infinite square well with exponential solution (of oscillatory type)?

Given a potential well of $V = 0$ on the interval $(0,L)$ and $V = \infty$ outside the well, I am working to solve the Time Independent Schrodinger Equation $$\dfrac{d^2}{dx^2} \psi= ...
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0answers
32 views

Valence bond wavefunction of nitrogen

Could someone explain to me how one finds the valence bond wavefunction of an atom? Take nitrogen for example, I know both nitrogen molecules have a valence-electron configuration of 2s22p1x2p1y2p1z ...
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2answers
72 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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1answer
63 views

QM: Why is there a minus sign on the Energy operator when using complex conjugate?

I understand how they get the first equation. But I have no idea why there is a minus sign on the second equation: This is from a derivation for the probability density current found here: ...
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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 ...
0
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1answer
93 views

Is there something wrong with quantizing two times in second quantization?

Second quantization is sometimes considered to be a bad name, because a single quantization is enough. For electrons, we can either start from a many body viewpoint and introduce field operators or we ...
2
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1answer
67 views

Help in solving Schrödinger equation for Hydrogen

I have almost finished getting the solution to the Schrödinger equation for the hydrogen atom (got the theta and phi component equations), but am stuck on the r component equation. Can anyone help me ...
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1answer
49 views

How do I take take the partial derivatives of the general solution to the TDSE for a free particle? [closed]

Consider the general solution to the time-dependent Schrödinger equation for a free particle \begin{align*} \Psi(x,t) &=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{+\infty} \phi(k) e^{i\left(\hbar ...
2
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1answer
36 views

Can someone clarify what should and should not be an operator in my verification of the 1D solution to the SE for a free particle?

I just worked out the 1D free particle solution to the Schrödinger equation. My wave function was \begin{equation} \psi(x,t) = Ae^{i(px-Et)/\hbar} \end{equation} So I plugged this into both sides ...
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4answers
184 views

Derivation of Schrödinger equation - free particle

I learn quantum physics from Alonso-Finn's book (Amazon link), there's one step of Schrödinger equation for a free particle that I couldn't understand. $$ \frac{\mathrm{d^{2}\Psi } }{\mathrm{d} ...
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3answers
123 views

Justifying the notation $\langle x\ |\ \psi\rangle$ [duplicate]

I came across this expression: $$\langle x\ |\ \psi\rangle=\psi(x)$$ How can it be justified? I understand the LHS as an inner product, and the RHS just as a function of the parameter $x$.
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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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3answers
104 views

Why is the expectation value of ground state electron momentum zero?

I have a normalized energy eigenfunction for the ground state of Hydrogen which is $$ \Psi(r) = \frac{1}{\sqrt{\pi a_0^3}}\exp\left(-\frac{r}{a_o}\right), $$ where $a_o$ is the Bohr radius, I have ...
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2answers
51 views

Why does a plane wave leave the position of the particle unspecified?

I'm covering a book on QM, and just started recently and I'm stuck at understanding something. It says that we can describe the state of motion of a particle with an infinite plane wave equation: ...
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4answers
136 views

What does “spread of momentum” actually mean?

I was reading Feynman's lecture in which Feynman invoked his own way of explaining the uncertainty principle using single-slit experiment. There I found: To get a rough idea of the spread of ...
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0answers
26 views

What are the conditions of wave function continuity when solving for Dirac Spinors as done in “Klein paradox” paper by Novoselov?

In the paper "Chiral tunneling and Klein paradox" paper by Katsnelson, Novoselov, and Geim, they use the wave function for Dirac spinors. What are the conditions for continuity of the wave function ...