Bijan Bagchi received his B.Sc., M.Sc., and Ph.D. degrees from the University of Calcutta. After Ph.D. he joined as an associate at the Raychaudhuri lab of Presidency College, Calcutta. Subsequently he went to the Institute for Theoretical Physics, University of Bern, Switzerland as a visiting scientist. A former Professor with the University of Calcutta he has served as its Head of the Department and also as the Coordinator of the UGC Special Assistance Programme. He later became a UGC Emeritus Fellow in the Department of Physics, Shiv Nadar University where he is currently holding the post of a Professor. Dr. Bagchi has held several research positions in Europe and the US including Visiting Professorships at Physique Nucleaire Theorique et Physique Mathematique, University of Libre, Brussels and also at Laboratoire de Physique et Chimie Theoriques, University of Lorraine, Metz, France and National Cheng Kung University, Tainan. During the past few years his research has focused in developing models for branched Hamiltonians, analysing group theoretic approach for rationally extended shape invariant potentials, carrying out a systematic quantitative study of generalised oscillators by casting them as model for dynamical systems and inquiring into the role of bi-complex Hamiltonians in quantum mechanics. He has published more than 150 research articles in various international and national journals in the area of theoretical physics and is the author of the books entitled Supersymmetry in Quantum and Classical Mechanics, Advanced Classical Mechanics and Partial Differential Equations for Mathematical Physicists, all published by the CRC Press, UK, respectively in the years 2000, 2017 and 2019.

** Research Interests:**

- Exactly and quasi exactly solvable systems
- Parity-time symmetry and pseudo-Hermitian models
- Lie algebraic techniques
- Supersymmetric quantum mechanics
- Non-commutative algebra
- Nonlinear dynamics
- Alternative theories of gravity, Dark matter and Dark energy
- Integrable systems

**Current research:**

We considered [1] the problem of determining the disentangled form of the evolution operator U(t) for a class of time-dependent non-Hemitian Hamiltonians. It was shown that this amounts to a transformation of the whole scheme in terms of addressing a nonlinear Riccati equation the existence of whose solutions depends on the fulfillment of a certain accompanying integrabilty condition. The evolution operator was constructed as the product of independent exponential operators by means of some Baker-Campbell-Hausdorff identities. The method was applied to a two level spin model.

Hamiltonians that are multivalued functions of momenta are of topical interest since they correspond to

the Lagrangians containing higher-degree time derivatives. Incidentally, such classes of branched

Hamiltonians lead to certain not too well understood ambiguities in the procedure of quantization.

Within this framework, we studied [2] some models sample the latter ambiguities and simultaneously

turns out to be amenable to a transparent analytic and perturbative treatment.

We considered [3] the rational extensions of two different parity (P)-time (T)-symmetric complex potentials, namely the

asymptotically vanishing Scarf II and asymptotically non-vanishing Rosen-Morse II potentials, and

obtained bound state eigenfunctions in terms of newly found exceptional class of Jacobi polynomials

and also some new type of orthogonal polynomials respectively. By considering the asymptotic

behaviour of the exceptional polynomials, we have obtained the reflection and transmission amplitudes for

them and discuss the various novel properties of the corresponding amplitudes.

We discussed [4] the parametric symmetries in different exactly solvable systems characterized by real

or complex PT-symmetric potentials. We focused attention on the conventional

potentials such as the generalized Poschl Teller (GPT), Scarf-I and PT-symmetric Scarf-II which are

invariant under certain parametric transformations. The resulting set of potentials were shown to yield a

completely different behavior of the bound state solutions. Further the supersymmetric partner

potentials acquire different forms under such parametric transformations leading to new sets of exactly

solvable real and also PT-symmetric complex potentials. These potentials were also observed to be

shape invariant. We subsequently studied the newly discovered rationally extended shape invariant

potentials, corresponding to the above mentioned conventional potentials, whose bound state solutions

are associated with the exceptional orthogonal polynomials (EOPs). We discussed the transformations of

the corresponding Casimir operator employing the properties of the underlying Lie algebra.

We investigated [5] bi-complex Hamiltonian systems in the framework of an analogous version of the

Schrodinger equation. Since in such a setting three different types of conjugates of bi-complex numbers

appear, each is found to define in a natural way, a separate class of time reversal operator. However,

the induced PT-symmetric models turn out to be mutually incompatible except for two of

them which could be chosen uniquely. The latter models were then explored by working within an

extended phase space. Applications to the problems of harmonic oscillator, inverted oscillator and

isotonic oscillator were considered and many new interesting properties were uncovered for the new

types of PT symmetries.

We derived [6] a one-step extension of the well known Swanson oscillator that describes a specific type

of pseudo-Hermitian quadratic Hamiltonian connected to an extended harmonic oscillator model. Our

analysis was based on the use of the techniques of supersymmetric quantum mechanics and addressed

various representations of the ladder operators starting from a seed solution of the harmonic oscillator

expressed in terms of a pseudo-Hermite polynomial. The role of the resulting chain of Hamiltonians

related via similarity transformation was then exploited. We also wrote down a two dimensional

generalization of the Swanson Hamiltonian and established superintegrability of such a system.

[1] B. Bagchi Lett. High Energy Physics 3 (2018) 04

[2] B.Bagchi, S.M.Kamil, T.Tummuru, I. Semoradova and M. Znojil J. Phys.A (Conf.Series) 839 (2017) 012011

[3] N.Kumari, R.K.Yadav, A.Khare, B.Bagchi and B.P.Mandal Annals of Physics 373, 163 (2016)

[4] R.K.Yadav, A.Khare, B.Bagchi, N.Kumari and B.P.Mandal J.Math.Phys.57,022701 (2016)

[5] B.Bagchi and A. Banerjee J.Phys.A (Math. and Theor.) 48, 505201 (2015)

[6] B.Bagchi and I. Marquette Phys.Lett. A 379 1584 (2015)

**Teaching at SNU:**

- Quantum Field Theory (PHY409)
- General Theory of Relativity (PHY413)
- Advanced Mathematical Methods for Physicists (PHY547)
- Review of Classical Mechanics (PHY506)
- Review of Quantum Mechanics (PHY508)

** Advisor:**

- Current PhD supervision: Dibyendu Ghosh on Branched Hamiltonians in Nonlinear Systems and Anindita Bera (jointly with Dr. Ujjwal Sen of Harish Chandra Research Institute, Allahabad) on Quantum Information Processing in Multiparty States.
- Undergraduate Supervision at SNU: Tarun Tummuru (2016-17), Siddhartha Seetharaman (OUR project 2016-17), Kabir Thakur (2017-18), Pranjal Agarwal (2018-19 current batch), Suvendu Barik (2018-19 current batch), B. Shyam Sunder (2018-19 current batch).

**SOME SELECTED PUBLICATIONS:**

- Quantum, noncommutative and MOND corrections to the entropic law of gravitation (with A. Fring), International Journal of Modern Physics B33 (2019) 1950018
- Non-standard Lagrangians and branching: the case of some nonlinear Liénard systems (with D. Ghosh, S. Modak and P.K. Panigrahi Modern Physics Letters A34 (2019) 1950110
- Evolution operator for time-dependnet non-Hermitian Hamiltonians Lett High Energy Physics 3 (2018) 04
- Scattering amplitudes for the rationally extended complex potentials (with N. Kumari, R.K.Yadav. A.Khare and B.P.Mandal) Annals of Physics 373, 163 (2016)
- Qualitative analysis of certain generalized classes of quadratic oscillator systems (with S. Ghosh, B. Pal and S. Poria
**)**Journal of Mathematical Physics 57,022701(2016) - Parametric symmetries in exactly solvable real and PT-symmetric complex potentials (with R.K.Yadav, A.Khare, N.Kumari and B.P.Mandal
**)**Journal of Mathematical Physics 57 062106 (2016). - Qualitative analysis of certain generalized classes of quadratic oscillator systems (with S. Ghosh, B. Pal and S.Poria) Journal of Mathematical Physics
**57**022701(2016). - Bicomplex Hamiltonian systems in quantum mechanics (with A.Banerjee) Journal of Physics A48 505201 (2015).
- Exploring branched Hamiltonians for a class of nonlinear systems (with S. Modak, P.K.Panigrahi, F. Ruzicka and M. Znojil) Modern Physics Letters A30 1550213 (2015).
- Rational extensions of trigonometric Poschl-Teller potential based on para-Jacobi polynomials (with Y. Grandati and C. Quesne) Journal of Mathematical Physics 56 062103 (2015).
- On Generalized Lienard oscillator and momentum dependent mass (with A Ghose Choudhury and P. Guha) Journal of Mathematical Physics 56 012015 (2015).
- New 1-step extension of the Swanson oscillator and superintegrability of its two-dimensional generalisation (with I. Marquette) Physics Letters A379 1584 (2015).
- Competing PT-potentials and re-entrant PT-symmetric phase for a particle in a box (with Y.Joglekar) Journal of Physics A45 402001 (2012 FTC).
- Minimal length in quantum mechanics and non-Hermitian Hamiltonian systems (with A. Fring) Physics Letters A373 4307 (2009).
- Existence of Different Intermediate Hamiltonians in Type A N-fold Supersymmetry (with T. Tanaka) Annals of Physics 324 2438 (2009)

** Service to Profession:**

- Frequent referee for a number of international journals in theoretical physics.
- Served on CSIR and UGC committees.
- Reviewer for fund proposals of DST, New Delhi.
- Expert of various selection committees in India and abroad.
- Member of PhD committee and Board of Studies of various Universities.
- Visiting Associate to Inter-University Centre for Astronomy and Astrophysics (IUCAA), Pune.
- Thesis evaluator for various Universities.

**Recent Academic Visits:**

- University of Vermont, Burlington, USA, May 2019
- University of Indianapolis, USA, May 2019
- University of Texas, Austin, May 2019
- Queen's College, CUNY, USA, May 2019