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Tagged with non-locality schroedinger-equation
5
questions
2
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0
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Relativistic Schrödinger Equation: How is it relativistic and can it be useful? [duplicate]
As is well known, the usual Schrödinger equation,
$$\mathrm{i}\hbar\frac{\partial}{\partial t}\psi=-\frac{\hbar^2}{2m}\Delta\psi+V\psi,$$
is not relativistic. It can be derived formally by applying ...
- 294
1
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2
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162
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How is the non-locality of a theory apparent from its mathematical form?
I am reading Relativistic Quantum Mechanics by Bjorken and Drell and on page 5 they present the following attempt at a relativistic Hamiltonian for a free particle
\begin{equation}
i\hbar\frac{\...
- 229
6
votes
1
answer
440
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Functional Analytic Square Root of Hamiltonian Alternative to Dirac
I was thinking about the history of the Dirac equation and asked myself, what happens if one simply considers the Schrödinger equation
$$i\hbar\frac{\partial\phi}{\partial t}=\sqrt{-c^2\hbar^2\Delta+m^...
- 3,915
3
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2
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Non-local potential
I read that the Schrodinger equation for a non-local potential is given by
$$-\frac{\hbar^2}{2m}\nabla^2\psi(x)+\int V(x,x')\psi(x')dx'=E\psi(x).$$
In case of a local potential,
$$ V(x,x')=V(x)\delta(...
- 158
10
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2
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What's wrong with the square root version of the Klein-Gordon equation?
The Wikipedia article has a derivation of the Klein-Gordon equation. It gets to this step:
$$\sqrt{\textbf{p}^2 c^2 + m^2 c^4} = E$$
and inserts the QM operators to get
$$\left( \sqrt{ (-i \hbar \...
- 2,979