10-16 June 2018
Dalhousie University
America/Halifax timezone
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An Analytic Approach for the Energy Eigenvalues Solutions in a Double-Well Potential

12 Jun 2018, 08:00
15m
McCain 2017 (cap.36) (Dalhousie University)

McCain 2017 (cap.36)

Dalhousie University

Oral (Non-Student) / Orale (non-étudiant(e)) Theoretical Physics / Physique théorique (DTP-DPT) T1-4 Mathematical Physics (DTP) | Physique mathématique (DPT)

Speaker

Prof. Sree Ram Valluri (Uuniversity of Western Ontario)

Description

Studies on scattering of longitudinally and transversely incident beam of electrons by hollow cylindrical potential and coaxial cylindrical potentials have shown the presence of quasi bound “whispering” modes [1,2]. The realization of Levinson’s theorem [3,4] has been studied for some scattering potentials and results are widely available.

Roberts and Valluri [5] presented a geometric analytic technique, which utilizes conformal mapping W->Z=We^W between two complex domains to solve the 1-dimensional finite square well potential. The symmetry of the hollow cylindrical potential can be used to solve the Schrodinger equation as a 1-dimensional finite square well potential in the radial direction. This leads to the possible generalization to a concentric double walled cylindrical potential by considering it as a double well finite potential in the radial direction. The number of bound states of such a potential can be counted using the Lambert W formalism, as it is a geometric method, and the relation to the scattering phase shift can be established.

References:

1) Vivishek Sudhir and P. C. Deshmukh
Scattering of electrons off hollow cylindrical potentials
J. Comput. Theor. Nanosci. 7, 2036 (2010)

2) Vivishek Sudhir and P. C. Deshmukh
Scattering of electrons by multi-walled cylindrical potentials
J. Comput. Theor. Nanosci. 8, 2321 - 2326 (2011)

3) N. Levinson
On the uniqueness of the potential in a Schrodinger equation for a given asymptotic phase
Danske Vid. Selsk. Mat.-Fys. Medd. 25:9 (1949)

4) C.J.Joachain
Quantum Collision Theory
North Holland, Amsterdam (1975)

5) Roberts and S.R. Valluri
The quantum finite square well and the Lambert W Function
Can. J. Phys. 95: 105-110 (2017)

Primary authors

Prof. Sree Ram Valluri (Uuniversity of Western Ontario) Dr Ken Roberts (University of Western Ontario) Dr Pranawa Deshmukh (Indian Institute of Technology, Tirupati) Mr Harsh Narola (Indian Institute of Science Education Research, Tirupati.) Dr Rob Scott (University of Brest) Dr Shantanu Basu (University of Western Ontario)

Presentation Materials