Please check whether my understanding is right or not timede

2-2 The Schrödinger Equation 3) Time-dependent equation h2 82 ihDt9(x, t) =2m0r2$(z, t) + V@w(x, t) ih_(x, t) = 4) Time independent equation (equation for standing waves) H: Hamiltonian operator E: energy of electron Vectorial Scalar -Wis an eigen function Different orbitals have different y, functions and different values of E 15

Solution

When we apply time dependent/independent Schrodinger wave equation:

When we are finding the characteristics of a particle, we will check the nature of the potential of the zone where the particle resides .

If the potential ( restrictions on the partilce in that zone) varies with time ( a charge particle in an alternating electric field) , we apply time dependent wave equation to find the wave function and where the potential is not depending on time ( eg. free particle or a charge particle in a dc field ), we apply time independent wave equation .

When a particle confined in a box, we will always get a standing wave pattern. Remember we calculate wave function from Schrodinger wave equation. So unless and untill we solve the equation we do not have any idea about the wave function. So we first look at the potential of the zone. Seeing the time dependency of the potential in that zone we apply Schrodinger wave equation (time dependent/time independent) accordingly...from their we obtain the wave function