Abstract
We focus on one of the Schrödinger operators called the Bochner– Laplacian. Using Jensen’s Formula and Vandermonde convolution, we show directly that for each k = 0, 1, 2, . . . , the number of Lagrangian submanifolds which satisfy the Maslov quantization condition is just equal to the multiplicity of the kth eigenvalue of the operator.
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Kanazawa, T. (2019). A Direct Proof for an Eigenvalue Problem by Counting Lagrangian Submanifolds. In: Kielanowski, P., Odzijewicz, A., Previato, E. (eds) Geometric Methods in Physics XXXVII. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-34072-8_18
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DOI: https://doi.org/10.1007/978-3-030-34072-8_18
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-34071-1
Online ISBN: 978-3-030-34072-8
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