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harmonic_oscillator_hamiltonian [2016/08/30 20:37] nikolaj old revision restored (2016/08/30 20:34) |
harmonic_oscillator_hamiltonian [2016/08/31 15:32] nikolaj |
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| === Discussion === | === Discussion === | ||
| + | == Remark == | ||
| + | Another "quantum harmonical oscillator" is a model which looks similar, except $x$ is an operator $x(t)$ (and one a priori more general than right multiplication by $x$ as here) and where instead of $\dfrac{\partial}{\partial x}$ we consider $\dfrac{1}{L^2}x'(t)$. In this case, we can may have $\kappa$ depend on $t$ too. | ||
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| + | It's basically a matter on how the $a$'s end up looking and in what way they relate to the ground state of the system. | ||
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| == Interpretation == | == Interpretation == | ||
| We describe a system with 1-dim degree of freedom, $x$, and a potential with no degrees of freedom. The "spring constant" $\kappa$ in the "interaction term" with $\kappa\cdot x$ quantifies the penalty for $x$ being away from $x_0$. | We describe a system with 1-dim degree of freedom, $x$, and a potential with no degrees of freedom. The "spring constant" $\kappa$ in the "interaction term" with $\kappa\cdot x$ quantifies the penalty for $x$ being away from $x_0$. | ||
