Question

What is the physical significance of time-independent & time-dependent schrodinger wave equation?

Answer 1

@eliassaab @amistre64 @ganeshie8 @Compassionate @nincompoop @gorv @skullpatrol

Answer 2

Simply,The time-dependent Schrödinger equation, is used to find the time dependence of the wavefunction.
u can also say that, here the potential energy depends on time, so the wave equation describes the change of position of the particle with time

Answer 3

and for time independent state, potential energy of the particle does not depend on time explicitly
so , in this case u can say this wave equation describes only the position of the particle

Answer 4

another point is-
The time-independent Schrodinger equation is mainly useful for describing standing waves but It has serious shortcomings when used to describing traveling waves

Answer 5

need more clarification?

Answer 6

if u need any applications then the best will be--Harmonic Oscillator
in this device time indepence of waves are used to detect standing waves

Answer 7

this is A significance of Time-ind scho. equation

Answer 8

For a non-radiating system, H is independent of time, would you explain this?

Answer 9

i mean hamiltonian

Answer 10

thanks for explaining me earlier

Answer 11

yeah thats a basic property
to prove it u need to know some basic properties of hamiltonians
\[H=H(p_1,p_2,...,p_k,q_1,q_2,...,q_k,t)\\=H(p_k,q_k,t)\\now ~taking~time~derivative\\ \frac{ dh }{ dt }=\sum_{k}^{}\frac{ \partial H }{ \partial q_k }q_k^{.}+\sum_{k}^{}\frac{ \partial H }{ \partial p_k }p_k^{.}+\frac{ \partial H }{ \partial t}\]

Answer 12

are u familiar with these?

Answer 13

yes

Answer 14

now u need to use these properties--
\[\frac{ \partial H }{ \partial q_k }=-p_k^{.}\\ \frac{ \partial H }{ \partial p_k }=q_k^{.}\]
apply these in the above equation

Answer 15

hey i'll be back by a hour then i'll complete the proof okay!!

Answer 16

okay...,