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arXiv · 1803.01597

Divergence of $\langle p^6\rangle$ in discontinuous potential wells

Zafar Ahmed·Sachin Kumar·Dona Ghosh·Joseph Amal Nathan
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Abstract

The surprising divergence of the expectation value $<\!p^6\!>$ for the square well potential is known. Here, we prove and demonstrate the divergence of $<\!p^6\!>$ in potential wells which have a finite jump discontinuity; apart from the square-well two-piece half-potentials wells are examples. These half-potential wells can be expressed as $V(x)=-U(x) \Theta(x)$, where $\Theta(x)$ is the Heaviside step function. $U(x)$ are continuous and differentiable functions with minimum at $x=0$ and which may or not vanish as $x\sim \infty$.

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Zafar Ahmed, Sachin Kumar, Dona Ghosh, Joseph Amal Nathan. 2018-03-05. Divergence of $\langle p^6\rangle$ in discontinuous potential wells. https://doi.org/10.1088/1361-6404%2Faac988

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