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POTENTIAL MORPHING METHOD (PMM)

 The code is available on request (contact Prof Dr. S. Baskoutas This email address is being protected from spambots. You need JavaScript enabled to view it. )

 

Potential Morphing Method (PMM) is a new method which has been developed for the quantum-mechanical determination of the eigenstates and eigenvalues of a particle in a potential of general shape. It is based on the quantum adiabatic theorem that concerns the dynamic evolution of quantum mechanical systems and states that if the Hamiltonian of the system varies slowly with time, then the n th eigenstate of the initial Hamiltonian will be carried into the n th eigenstate of the final Hamiltonian. For the application of this method any well-known reference system is needed.

"Exact Numerical Solution of Schrödinger's equation for a particle in an interaction potential of general shape" 
M. Rieth, W. Schommers, S. Baskoutas, Int. J. Mod. Phys. B 16, 4081 (2002).

 

The PMM method has been applied for the estimation of structural properties of nanomaterials such as quantum wells, quantum wires and quantum dots.

For example PMM method has already been applied for the calculation of:

Size Dependent Band Gap of various Colloidal Quantum Dots.

In this case introducing the Hartee-Fock approximation the exciton energy is estimated in the effective mass approximation.

The method has shown good results for wide band gap semiconductor quantum dots.
"Size-dependent band gap of colloidal quantum dots"
S. Baskoutas, A. F. Terzis, Journal of Applied Physics 99, 013708 (2006).

and for narrow band gap semiconductor quantum dots.
"Size-Dependent Exciton Energy of Narrow Band Gap Colloidal Quantum Dots in the Finite Depth Square-Well Effective Mass Approximation"
S. Baskoutas, A. F. Terzis, W. Schommers, Journal of Computational and Theoretical Nanoscience 3, 269 (2006).

 

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