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What Kind of Insight Provide Analytical Solutions of Quantum Models?
[chapter]

2020
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Mathematics for Industry
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There are several concepts of what constitutes the analytical solution of a quantum model, as opposed to the mere "numerically exact" one. This applies even if one considers only the determination of the discrete spectrum of the corresponding Hamiltonian, setting aside such important questions as the asymptotic dynamics for long times. In the simplest case, the spectrum can be given in closed form, the eigenvalues $$E_{j}, j=0,\ldots ,N\le \infty $$ read $$E_{j} =f(j,\{p_{k}\})$$, where f is a

doi:10.1007/978-981-15-5191-8_2
fatcat:pzov2vef2vggnhjmpnnbnnev6u