What is the difference between time dependent and time independent?

The time dependant equation describes how the wavefunction evolves in time and space and relates the two. You can solve the equation for specified potentials. The time independent equation on the other hand, describes how the wavefunction evolves in space and relates it to the energy of a state.

What is time independent perturbation theory?

Abstract. Time-independent perturbation theory is an approximation scheme that applies in the following context: we know the solution to the eigenvalue problem of the Hamiltonian H0, and we want the solution to H = H0 +H1 where H1 is small compared to H0 in a sense to be made precise shortly.

What is Schrödinger time independent and time dependent wave equation?

The Schrodinger equation is the name of the basic non-relativistic wave equation used in one version of quantum mechanics to describe the behavior of a particle in a field of force. There is the time-dependent equation used for describing progressive waves, applicable to the motion of free particles.

What is difference between degenerate and non degenerate perturbation theory?

In quantum mechanical words if two or more eigen functions correspond to the same eigen value they are said to be degenerate. Here, there is only one state with the energy and is described by a specific eigen function or wave function. Such states are called non-degenerate states.

What is time independent equation?

The time-independent Schrodinger equation is used for a number of practical problems. Systems with bound states are related to the quantum mechanical “particle in a box”, barrier penetration is important in radioactive decay, and the quantum mechanical oscillator is applicable to molecular vibrational modes.

What is the use of time dependent Schrodinger equation?

The probability of a transition between one atomic stationary state and some other state can be calculated with the aid of the time-dependent Schrödinger equation.

What is the validity of time independent perturbation theory?

First order perturbation theory will give quite accurate answers if the energy shifts calculated are (nonzero and) much smaller than the zeroth order energy differences between eigenstates. If the first order correction is zero, we will go to second order.

What is the purpose of perturbation theory?

There is a general method of calculating these errors; it is called perturbation theory. One of the most important applications of perturbation theory is to calculate the probability of a transition between states of a continuous spectrum under the action of a constant (time-independent) perturbation.

What is Schrödinger wave equation derivation?

The Schrodinger equation is derived to be the condition the particle eigenfunction must satisfy, at each space-time point, in order to fulfill the averaged energy relation. Effectively, the Schrodinger and Dirac equations are space-time versions of the respective averaged energy relations.

What is the difference between degeneracy and non degeneracy?

The dimension of the eigenspace corresponding to that eigenvalue is known as its degree of degeneracy, which can be finite or infinite. An eigenvalue is said to be non-degenerate if its eigenspace is one-dimensional.

What is the difference between degenerate and non-degenerate orbitals?

Orbitals with the same energy are called degenerate. When you move to a lonely helium atom, the orbitals in the subshells are degenerate. When you make chemical bonds, the orbitals in subshells are no longer degenerate. When you apply a magnetic field, the electrons in the same orbital are not degenerate.