All Questions
Tagged with wavefunction hamiltonian
98
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Connection between dispersion relation and symmetries of the Hamiltonian
I am having trouble understanding intuitively the connection between the dispersion relation and the symmetries of the Hamiltonian. For example, suppose we have a lattice and there are four sub-...
- 324
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Eigenstates of the Laplacian and boundary conditions
Consider the following setting. I have a box $\Omega = [0,L]^{d} \subset \mathbb{R}^{d}$, for some $L> 0$. In physics, this is usually the case in statistical mechanics or some problems in quantum ...
- 1,131
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2
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83
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Why is the time derivative of the wavefunction proportional to a linear operator on it? [closed]
I am currently trying to self-study quantum mechanics. From what I have read, it is said that knowing the wave function at some instant determines its behavior at all feature instants, I came across ...
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Is the overall (distinguishble-particle) ground state for a many-body identical particle Hamiltonian also immediately the bosonic ground state?
Consider the following many-body Hamiltonian of $N$ particles in an external trapping potential with inter-particle interactions:
\begin{align}
\hat{H}= \sum_{i=1}^{N} \left[-\frac{\hbar^2}{2m} \...
- 121
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Is the initial state the eigenstate of a Hamiltonian?
Solutions to the Schrödinger equation can take the form $ \psi(r,t)=\psi(r)f(t) $, where $f(t) = e^{\frac{-iEt}{\hbar}}$,
$$ H \psi(r) = E \psi(r) ,$$ where $\psi(r)$ is the eigenstate of a ...
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How to measure the Hydrogen wavefunction from an inertial frame in motion?
I want to calculate how the wave function evolves for a hydrogen atom in its lowest energy state ($n=1$) if its center of mass is moving with a relativistic low-speed $v$.
I expect, of course, that ...
- 403
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4
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613
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Hamiltonian Operator
I've learned that the Hamiltonian Operator corresponds to the total energy of the system when applied to a general wave function. After applying and obtaining the measurement (energy), the wave ...
user381511
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130
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Eigenfunctions of time-independent Hamiltonians
My Question is about the following theorem, which we use often in our quantum theory lecture:
I'm sticking to one-dimensional problems for this question.
Eigenfunctions of hermitian Operators on $L^2(\...
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When solving the Schrodinger Equation, where do we add the condition that $E$ is real?
I'm reading through Griffiths, and I noticed two seemingly contradictory facts:
In Chapter 1, it is proved that for any square-integrable function solving the Schrodinger Equation, $$\frac{d}{dt}\...
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Why is the full Hamiltonian used instead of the approximate Hamiltonian for determining the effective nuclear charge using the variational principle?
My question is in regards to the variational principle in approximating the wavefunction of Helium.
Some Background:
$$\hat{H}=-\frac{\hbar^2}{2m_{e}}\nabla_{1}^{2}-\frac{\hbar^2}{2m_{e}}\nabla_{2}^{2}...
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Time Independent Schrödinger Equation meaning
Working on some QM and we realised we don't understand the simple equation is for the wavefunction.
$H \psi(x) = E \psi(x)$
We know $H$ is the hamiltonian, the sum of the kinetic and potential ...
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0
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Replacing the box with a harmonic oscillator and finding the wave function? [closed]
I'm trying to strengthen my knowledge of quantum mechanics in general. Given a normalized free particle in a box eigenfunction as an initial condition:
$$\psi(x,0) = \begin{cases} \frac{1}{\sqrt{2}} \...
- 1,324
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1
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68
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How would a free particle with known spin evolve?
I searched a lot for a Hamiltonian of a pauli spinor with no potential energy but got no luck, so I tried deriving one my own.
I took an overkill shortcut and used pauli's equation:
$$i\hbar \frac{\...
- 1,324
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2
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272
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In Quantum Mechanics is it possible to apply time evolution operator to wavefunction?
If I consider a wavefunction that is the superposition of Hamiltonian eigenfunctions, for example like: $$\psi(x)=\frac{1}{\sqrt{2}}\psi_1(x)+\frac{1}{\sqrt{2}}\psi_2(x)$$ with $\hat{H}\psi_1(x)=E_1\...
- 35
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Does this relativistic generalization of the Schrodinger equation make sense? [duplicate]
So I'm aware that the correct relativistic approach to quantum mechanics is through quantum fields, but I'm still interested in the question that follows.
We know the Schrodinger equation in free ...
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