Question

\[\frac{\partial^2 \psi}{\partial x^2}+\frac{\partial^2 \psi}{\partial y^2}+\frac{\partial^2 \psi}{\partial z^2}+\frac{8 \pi ^2 m}{h^2}(E-V) \psi =0.\] Shrodinger Equation.

Answer 1

wt does this actually mean?
wt are the solutions?

Answer 2

wave function are solutions

Answer 3

so
\[\psi \space; \space \psi ^2\] are solutions ??????

Answer 4

do you want a text to read?

Answer 5

no; i have read already but couldn't understand.
but wanna understand from helpers as u:)

Answer 6

The time dependent wavefunction
\[\Psi(x,t)=\psi(x)\phi(t)\]
is normalized
\[\int\limits_{-\infty}^\infty\left|\Psi(x,t)\right|^2\text dx=1\]

Answer 7

wt is the meaning of this ?

Answer 8

i think u have broken the function as a product of 2 other functions
but wt about the integral?

Answer 9

you have quoted thee dimensional time independent schrödinger equation

Answer 10

the mod square of Psi
is Psi times its complex conjugate,
\[\left|\Psi\right|^2=\Psi^*\Psi\]
the time variable will go because
\[\psi(t)=e^{iEt/\hbar}\]

Answer 11

\[\sum\limits_{j=0}^\infty P_j=1\]the sum of probabilities is equal to one \[\int\limits_{-\infty}^{\infty}|\Psi(x,t)|^2=\int\limits_{-\infty}^{\infty}\rho(x)=1\]

Answer 12

so this equation contains infinite solution but when broken in two parts have wave function as its solution??????????
Am i right????????

Answer 13

i think you are right , the psi's are the solutions yes

Answer 14

very few people actually know whta he hel it is rest are just memorizing and using it and i hate it. . . :P
because me too can't understand it because no one is really there to explain n simple words. . .
i would advice you to put this question in physics forum.

Answer 15

ok thanx a lot
but plz tell me how this equation works in finding orbitals?

Answer 16

orbitals are the shapes of the solution

Answer 17

oh i see
thanx once again:)

Answer 18

this equation expresses potential energy of the patical as well kinetic energy wrt all theree dimensions that is x, y, and z. . .
this equation contains all these terms. . .

Answer 19

of course there are infinite solutions but there is higher probability density where the cloud of solutions is less faint(dense)

Answer 20

less faint ; more dense

Answer 21

ok i gt
so
\[\psi^2 \] is our probility density:)

Answer 22

\[\rho(x,y,z) \]is this spacial density

Answer 23

your pretty close it is the mod square of Psi
\[|\Psi(t,x,y,x)|=\Psi(t,x,y,x)^*\Psi(t,x,y,x)\]

Answer 24

=\(\rho(x,y,z)\)

Answer 25

oh ok i gt
thanx:)

Answer 26

QM uses \(a^*\) to denote the complex conjugate of \(a\)
you might be more familiar with
\(\overline a\)

Answer 27

if \(z=a+ib\)\[\overline z=z^*=a-ib\]

Answer 28

ok!