Geodesic
An n-dimensional pseudo-differential operator involving linear canonical transform and some applications in quantum mechanics
Filomat, Tome 37 (2023) no. 13, p. 4155

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DOI

In this work, an n-dimensional pseudo-differential operator involving the n-dimensional linear canonical transform associated with the symbol σ(x 1 ,. .. , x n ; y 1 ,. .. , y n) ∈ C ∞ (R n × R n) is defined. We have introduced various properties of the n-dimensional pseudo-differential operator on the Schwartz space using linear canonical transform. It has been shown that the product of two n-dimensional pseudo-differential operators is an n-dimensional pseudo-differential operator. Further, we have investigated formal adjoint operators with a symbol σ ∈ S m using the n-dimensional linear canonical transform, and the L p (R n) boundedness property of the n-dimensional pseudo-differential operator is provided. Furthermore, some applications of the n-dimensional linear canonical transform are given to solve generalized partial differential equations and their particular cases that reduce to well-known n-dimensional time-dependent Schrödinger-type-I/Schrödinger-type-II/Schrödinger equations in quantum mechanics for one particle with a constant potential.
DOI : 10.2298/FIL2313155P
Classification : 47G30, 46A11, 53D22, 35Bxx, 35Q41
Keywords: Pseudo-differential operator, Schwartz space, Linear canonical transform, Generalized solutions to partial differential equations, Time-dependent Schrödinger equations 
Tusharakanta Pradhan; Manish Kumar. An n-dimensional pseudo-differential operator involving linear canonical transform and some applications in quantum mechanics. Filomat, Tome 37 (2023) no. 13, p. 4155 . doi: 10.2298/FIL2313155P
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     title = {An n-dimensional pseudo-differential operator involving linear canonical transform and some applications in quantum mechanics},
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     doi = {10.2298/FIL2313155P},
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