Abstract:In the present note, we uncover a remarkable connection between the length of periodic orbit of a classical particle enclosed in a class of 2-dimensional planar billiards and the energy of a quantum particle confined to move in an identical region with infinitely high potential wall on the boundary. We observe that the quantum energy spectrum of the particle is in exact oneto-one correspondence with the spectrum of the amplitude squares of the periodic orbits of a classical particle for the class of integrable… Show more
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