On Singular Potential of the Schrödinger Equation

Autor:	Miyuki Nishikawa
Rok vydání:	2003
Předmět:	Essential singularity Physics Nuclear and High Energy Physics General Physics and Astronomy Astronomy and Astrophysics Function (mathematics) Eigenfunction Schrödinger equation Momentum Renormalization symbols.namesake symbols Quantum gravity Gravitational singularity Mathematical physics
Zdroj:	Modern Physics Letters A. 18:1991-1999
ISSN:	1793-6632 0217-7323
DOI:	10.1142/s0217732303011885
Popis:	In usual dimensional counting, momentum has dimension one. But a function f(x), when differentiated n times, does not always behave like one with its power smaller by n. This inevitable uncertainty may be essential in general theory of renormalization, including quantum gravity. As an example, we classify possible singularities of a potential for the Schrodinger equation, assuming that the potential V has at least one $C^2$ class eigen function. The result crucially depends on the analytic property of the eigen function near its 0 point.
Databáze:	OpenAIRE
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