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Results tagged with quantum-mechanics
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user 294547
Quantum mechanics describes the microscopic properties of nature in a regime where classical mechanics no longer applies. It explains phenomena such as the wave-particle duality, quantization of energy, and the uncertainty principle and is generally used in single-body systems. Use the quantum-field-theory tag for the theory of many-body quantum-mechanical systems.
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Spherical Harmonics and the Salpeter Eq $i\hbar\frac{\partial\Psi}{\partial t}=\left(E_0\sqr...
Recall the spinless Salpeter equation
$$
i\hbar \frac{\partial \Psi}{\partial t} = \left(E_0\sqrt{1-L_0^2 \Delta}+\frac{kZ}{r}\right) \Psi(r, \theta, \phi, t)
$$
where $E_0 = mc^2$, $L_0 = \frac{\hbar …
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Solving the 1D Schrödinger equation under the potential $V(x) = f(t)x$ [closed]
Following the sketch given in this answer, I hoped to solve the 1+1 dimensional Schrodinger equation under a potential $f(t)x$ by using a time dependent boost.
$$\left(\frac{-\hbar^2}{2m}\frac{\partia …
- 185
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Schrodinger Equation: Time Dependent, Periodic Potential $$V(x,t)=\begin{cases}V_0x&:t\in[0,...
Imagine that we have a particle in a cylinder of finite length and neglible radius. We can then assume that the system is axisymmetric and can be solved in one dimension.
Let us consider a time varyin …
- 185
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Notation in the Liouville-von Neumann equation $ i\hbar\frac{dI}{dt} = i\hbar\frac{\partial ... [duplicate]
The Liouville-von Neumannn equation is defined by
$$
i\hbar\frac{dI}{dt} = i\hbar\frac{\partial I}{\partial t} + [I, H]
$$
where $I$ is any operator and $H$ is the Hamiltonian. I assume that the left- …
- 185