Solution Of A Quantum Evolution Equation Using A Unitary Group Of Operators
ABSTRACT
An equation describing the change of the
state of a quantum system with respect to time is called a time evolution
equation. One of the fundamental evolution equation of quantum mechanics is the
Schrodinger equation; a dynamical system that has yielded closed form solution
only in specialized and simplified cases. By observing that the
time-independent Hamiltonian for the system is provided by a one parameter
group of unitary operators, we cast the evolution equation within the frame
work of this group of unitary operators, and thus obtained close form solutions
for the time-dependent case, the equation dynamics specified a Hamiltonian that
is the sum of two terms, a perturbed and the unperturbed part. The solution for
the perturbed part was obtained in the form of an integral equation which can
be iteratively constructed. The exact solution for the unperturbed part was
obtained and probability that at time t the system can be found in a specific state
0.0
EKWOMCHI, H (2022). Solution Of A Quantum Evolution Equation Using A Unitary Group Of Operators. Repository.mouau.edu.ng: Retrieved Nov 22, 2024, from https://repository.mouau.edu.ng/work/view/solution-of-a-quantum-evolution-equation-using-a-unitary-group-of-operators-7-2
HANNAH, EKWOMCHI. "Solution Of A Quantum Evolution Equation Using A Unitary Group Of Operators" Repository.mouau.edu.ng. Repository.mouau.edu.ng, 19 Oct. 2022, https://repository.mouau.edu.ng/work/view/solution-of-a-quantum-evolution-equation-using-a-unitary-group-of-operators-7-2. Accessed 22 Nov. 2024.
HANNAH, EKWOMCHI. "Solution Of A Quantum Evolution Equation Using A Unitary Group Of Operators". Repository.mouau.edu.ng, Repository.mouau.edu.ng, 19 Oct. 2022. Web. 22 Nov. 2024. < https://repository.mouau.edu.ng/work/view/solution-of-a-quantum-evolution-equation-using-a-unitary-group-of-operators-7-2 >.
HANNAH, EKWOMCHI. "Solution Of A Quantum Evolution Equation Using A Unitary Group Of Operators" Repository.mouau.edu.ng (2022). Accessed 22 Nov. 2024. https://repository.mouau.edu.ng/work/view/solution-of-a-quantum-evolution-equation-using-a-unitary-group-of-operators-7-2