- #1
tjsgkdms1111
Homework Statement
ca(0)=1, cb(0)=0
zeroth: ca(t)=1, cb(t)=0
1st: ca(t)=1, cb(t)=i/hbar*integral(H'(t) exp(iwt)) dt
ca^2+cb^2=1 to 1st order of H'.: What does it mean?
it is evidently not 1 at all.
Is this really a homework question, or you don't understand something about TDPT?tjsgkdms1111 said:Homework Statement
ca(0)=1, cb(0)=0
zeroth: ca(t)=1, cb(t)=0
1st: ca(t)=1, cb(t)=i/hbar*integral(H'(t) exp(iwt)) dt
ca^2+cb^2=1 to 1st order of H'.: What does it mean?
it is evidently not 1 at all.
Homework Equations
The Attempt at a Solution
The Griffith Intro to QM course is an introductory course in quantum mechanics that covers the basic principles and mathematical framework of the field. It also includes an introduction to first-order perturbation theory in time-dependent systems.
Perturbation theory in quantum mechanics is a mathematical tool used to approximate solutions to complex quantum systems by adding a small perturbation to a known, solvable system. It is particularly useful for understanding the behavior of systems that are subject to external influences or time-dependent changes.
First-order perturbation theory in time-dependent systems is a specific application of perturbation theory that allows for the calculation of the effects of a small, time-dependent perturbation on a quantum system. It involves expanding the time-dependent wave function in terms of the unperturbed wave functions and using time-dependent perturbation theory to calculate the coefficients of the expansion.
Perturbation theory is important in quantum mechanics because it allows for the calculation of approximate solutions to complex systems that would otherwise be impossible to solve exactly. It is also a useful tool for understanding the effects of external influences or time-dependent changes on quantum systems.
First-order perturbation theory in time-dependent systems can be applied to a wide range of real-world problems, such as the behavior of atoms and molecules in electromagnetic fields, the interaction between light and matter, and the dynamics of chemical reactions. It is also used in fields such as solid-state physics, nuclear physics, and particle physics to understand the behavior of quantum systems.