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Ski de fond

Alain Dufresnoy (1983/1984)

Séminaire de théorie spectrale et géométrie

Solution of Space-Time Fractional Schrödinger Equation Occurring in Quantum Mechanics

Saxena, R., Saxena, Ravi, Kalla, S. (2010)

Fractional Calculus and Applied Analysis

Dedicated to Professor A.M. Mathai on the occasion of his 75-th birthday. Mathematics Subject Classi¯cation 2010: 26A33, 44A10, 33C60, 35J10.The object of this article is to present the computational solution of one-dimensional space-time fractional Schrödinger equation occurring in quantum mechanics. The method followed in deriving the solution is that of joint Laplace and Fourier transforms. The solution is derived in a closed and computational form in terms of the H-function. It provides an elegant...

Solution of the Neumann problem for the Laplace equation

Dagmar Medková (1998)

Czechoslovak Mathematical Journal

For fairly general open sets it is shown that we can express a solution of the Neumann problem for the Laplace equation in the form of a single layer potential of a signed measure which is given by a concrete series. If the open set is simply connected and bounded then the solution of the Dirichlet problem is the double layer potential with a density given by a similar series.

Solvability Conditions for a Linearized Cahn-Hilliard Equation of Sixth Order

V. Vougalter, V. Volpert (2012)

Mathematical Modelling of Natural Phenomena

We obtain solvability conditions in H6(ℝ3) for a sixth order partial differential equation which is the linearized Cahn-Hilliard problem using the results derived for a Schrödinger type operator without Fredholm property in our preceding article [18].

Some estimates concerning the Zeeman effect

Wiesław Cupała (1993)

Studia Mathematica

The Itô integral calculus and analysis on nilpotent Lie grops are used to estimate the number of eigenvalues of the Schrödinger operator for a quantum system with a polynomial magnetic vector potential. An analogue of the Cwikel-Lieb-Rosenblum inequality is proved.

Some remarks on the Weyl asymptotics by the approximate spectral projection method

Ernesto Buzano (2000)

Bollettino dell'Unione Matematica Italiana

In questo lavoro studiamo il resto relativo della formula asintotica per gli autovalori di un operatore differenziale in R n , ottenuta mediante il metodo delle proiezioni spettrali approssimate ([3], Theorem 6.2). In un primo tempo diamo un controesempio di un operatore di Schrödinger con potenziale a crescita algebrica, per il quale il resto non è limitato. Quindi specifichiamo alcune condizioni addizionali da imporre all'operatore in modo da avere un resto infinitesimo.

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