A class of GUP solutions in deformed quantum mechanics

Understand

Various candidates of quantum gravity such as string theory, loop quantum gravity and black hole physics all predict the existence of a minimum observable length which modifies the Heisenberg uncertainty principle to so-called Generalized Uncertainty Principle (GUP).

• This approach results in the modification of the commutation relations and changes all Hamiltonians in quantum mechanics.
• In this paper, we present a class of physically acceptable solutions for a general commutation relation without directly solving the corresponding generalized Schrodinger equations.
• These solutions satisfy the boundary conditions and exhibit the effect of the deformed algebra on the energy spectrum.