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arxiv: 1901.04025 · v1 · submitted 2019-01-13 · 🪐 quant-ph

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Comment on "The hard sphere quantum propagator: exact results via partial wave analysis''

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classification 🪐 quant-ph
keywords propagatorexactexpressionhardknownpartialspherewave
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There is no known exact expression for the propagator of a non-relativistic particle colliding with a hard sphere. De Prunel\'e (2008 {\it J.~Phys.~A:~Math.~Theor.} {\bf 41} 255305) derived a partial wave expansion of the propagator and compared it against some known approximations, including the semiclassical Van Vleck-Gutzwiller (VG) propagator; the VG propagator was evaluated entirely numerically. Here we point out that the VG propagator for the particle-sphere problem admits an analytic expression in terms of elementary functions.

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