Classical and quantum harmonic oscillators with time dependent mass and frequency: A new class of exactly solvable model

2017 ◽  
Vol 386 ◽  
pp. 37-42 ◽  
Author(s):  
Swapan Mandal
Keyword(s):  
Solvable Model ◽  
Harmonic Oscillators ◽  
Time Dependent ◽  
Exactly Solvable Model ◽  
New Class ◽  
Exactly Solvable ◽  
Dependent Mass

scholarly journals Trapping Charge Carriers in Low-Dimensional Dirac Materials

2019 ◽  
Vol 18 (03n04) ◽  
pp. 1940001
Author(s):  
C. A. Downing ◽  
M. E. Portnoi
Keyword(s):  
Bound States ◽  
Solvable Model ◽  
Mass Term ◽  
Bound State ◽  
Charge Carriers ◽  
Exactly Solvable Model ◽  
Dirac Materials ◽  
Exactly Solvable ◽  
Low Dimensional ◽  
Dependent Mass

We consider the problem of confining the famously elusive Dirac-like quasiparticles, as found in some recently discovered low-dimensional systems. After briefly surveying the existing theoretical proposals for creating bound states in Dirac materials, we study relativistic excitations with a position-dependent mass term. With the aid of an exactly-solvable model, we show how bound states begin to emerge after a critical condition on the size of the mass term is met. We also reveal some exotic properties of the unusual confinement discovered, including an elegant chevron structure of the bound state energies as a function of the size of the mass.

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