# Tagged Questions

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### Why can we leave off half of the general solution?

In these pdf notes, it says at the bottom of the first page and beginning of the second: [...] whose solution is: $$\Psi(\theta) = c_1 e^{i\omega\theta} + c_2 e^{-i\omega\theta}$$ Since we are ...
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### Correct approach for calculating excited states of circular quantum dot under effective mass approximation

From Asnani, Mahajan et al, Pramana Journal Of Physics 73 #3 (2009) p574-580 "Effective mass theory of a two-dimensional quantum dot in the presence of magnetic field", which can be seen here: ...
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### Particle Outside the Box

What prohibits, mathematically, that a particle cannot be found outside the box ? Here, I am referring to particle in a box problem (infinite potential on both ends & zero potential along the ...
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### Is there only radial motion in the Hydrogen ground state?

The ground state of the Hydrogen atom is spherically symmetric. In other words, the wave function Psi depends only on the distance r of the electron from the nucleus. As a consequence all ...
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### What is the difference between the Bohr model of the atom and Schrödinger's model?

What is the difference between the Bohr model of the atom and The solution of the Schrödinger equation for the hydrogen atom? Are there any difference between definition of the electric potential ...
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### System without ground state is not real in nature?

We know that Coulomb force is real phenomena in nature and with Coulomb potential $V(x) \thicksim -\frac{1}{|x|}$ lowest energy is bounded in hydrogen atom. But it's mathematically clear that if ...
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### 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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### Infinitely many degeneracy of Landau level: Countable or Uncountable?

Description of Landau levels can be found in many standard textbooks of quantum mechanics and here. Two ubiquitous solutions apply either the symmetric gauge $\vec{A}=(-\frac{1}{2}By,\frac{1}{2}Bx,0)$ ...
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### What does the Schrodinger Equation really mean?

I understand that the Schrodinger equation is actually a principle that cannot be proven. But can someone give a plausible foundation for it and give it some physical meaning/interpretation. I guess ...
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### Eigenfunctions for $1s$ hydrogen Schrodinger equation

I am a computer scientist and started my Phd in material science. The second course os my Phd is material simulation by computer. One the task is show the verification of the eigenfunction $1s$ from ...
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### Dependence of sign on operators in wave equation?

In the time-dependent Schrödinger equation, our teacher told us about energy and momentum operators. He just defined them, the equation was of the form $A\exp(i(kx-\omega t))$, if we take the ...
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### Am I missing a trick to solving this differential equation?

I was playing around with a 3-D potential $V$ such that $V_{(r)} = 0$ for $r<a$, and $V_{(r)} = V_0$ otherwise. By using the Schrödinger Equation, I showed that: ...
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### Uncertain if invoking uncertainty principle for wave function is handwaving [duplicate]

Why doesn't the electron collapse onto the proton in a hydrogen atom? One explanation seems to be given by the Heisenberg uncertainty principle, which follows from the purely physical assertion that ...
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### Justification of discrete spectrum for V(x) unbounded at $\pm \infty$ in Pauling and Wilson

In Pauling and Wilson, Introduction to Quantum Mechanics, they offer the following intuitive reason for the discrete spectrum of a potential which is unbounded at $\pm \infty$: This is ...
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### Proving that the electronic Schrödinger equation has no closed analytic solutions for >1 electron

It is stated in many books that analytic closed solutions to the time-independent electronic Schrödinger equation, $$\hat{H}\Psi = E\Psi,$$ exist for the one-electron problem (e.g. hydrogen atom, ...
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### Is there some quantum potential producing exponential eigenvalues?

Usual central potentials produce quantum spectra with energy levels going as $n$, $n^2$, $n^3$ and so on, being $n$ the quantum number of the orbit. In the other extreme we have "dirac-delta" ...
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### Does Heisenberg equation of motion imply the Schrodinger equation for evolution operator?

Let us choose to postulate (e.g. considering the analogy of the Hamiltonian being a generator of time evolution in classical mechanics) $$i\hbar \frac{d\hat{U}}{dt}=\hat{H}\hat{U}\tag{1}$$ where ...
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### Computational package to find the ground state of a particle in 3D domain

I am developing a numerical algorithm to find the ground state of a Hermitian matrix. Obvious applications are quantum many-body systems and particles in various potentials. I am a little stuck with ...
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### Solving the Schrödinger equation where the initial wave function is an energy eigenfunction

I was watching Allan Adams' lecture on energy eigenfunctions, and there's one part (around 43 minutes into the lecture) that confuses me. Suppose we have the initial wave function $\Psi (x,0)$ such ...
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### What is the energy operator and from where do we get it?

I am trying to learn Quantum mechanics from MIT OCW Videos about quantum mechanics. I have reached the 5th lecture. Please help me in understanding this: In the middle (At 32:08), the professor wrote ...
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### Poles for a particle scattered in a delta potential

I am working on problem a professor gave me to get an idea for the research he does, and have hit a point where I'm having a difficult time seeing where I need to go from where I'm at. I would also ...
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### Divergent solution in time-dependent Schrödinger equation

if I transform the time-dependent Schrödinger equation without a potential I get: $$- \hbar \omega \psi(\omega,x) = \frac{- \hbar^2}{2m} \frac{\partial^2 \psi(\omega,x)}{\partial x^2}$$ The ...
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### Initial condition for Fourier transformed Schrödinger equation

I asked in this thread Time-dependet Schrödinger equation how to solve the Time-dependent Schrödinger equation. One of JamalS' recommendations was the Fourier transform, which is why I want to quote ...