Volume 5, Issue 3, September 2019, Page: 52-57
Quantum Wave Function Based on String Theory for Frictional Medium to Obtain Collision Probability, Energy Operator and Schrodinger Equation
Asma Mohamed Elhussin, Qilwah College of Science and Arts, Department of Physics, Albaha University, Al Baha, Saudi Arabia
Received: Mar. 24, 2019;       Accepted: May 21, 2019;       Published: Aug. 12, 2019
DOI: 10.11648/j.ijamtp.20190503.11      View  8      Downloads  9
Schrodinger equation suffer from being not sensitive to the mechanical properties as well as the electric and magnetic properties of matter. This set back can be cured by starting the derivation using the function sensitive to these parameters. Treating particle as vibrating strings a useful expression for the velocity was found using the equation of motion. Then the relation of current density with a velocity and electric field intensity was utilized to obtain the electric field intensity in a frictional medium. Using the analogy of the electric field and quantum wave function, the wave function was obtained and found to give the conventional expression for the collision probability with relaxation time twice the classical one. Another approach was tackled by obtaining a useful expression of the total energy of strings for resistive collisional medium. This expression utilizes the wave function of quantum particle in a frictional medium to obtain collision probability formula. Fortunately this latter approach gives a relaxation time equal to the classical one. The same wave function is used to find Hamiltonian operator for the both steady state and perturbed state by friction. Fortunately both Hamiltonians satisfy hermiticty condition. The hermiticty condition for the perturbed states however needs splitting the Hamiltonian into unpertured and perturbed part.. The perturbed term satisfies uncertainty principle. The energy expression for the resistive medium resembles that of Einstein and RLC circuits. Schrodinger equation for the frictional medium was also found, where it reduces to the ordinary one when friction disappear.
String, Collision Probability, Relaxation Time, Energy Operator, Schrodinger Eqauation, Hermiticty
To cite this article
Asma Mohamed Elhussin, Quantum Wave Function Based on String Theory for Frictional Medium to Obtain Collision Probability, Energy Operator and Schrodinger Equation, International Journal of Applied Mathematics and Theoretical Physics. Vol. 5, No. 3, 2019, pp. 52-57. doi: 10.11648/j.ijamtp.20190503.11
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