Schrodingers equation

Question 1

Idea behind schrodingers:

Answer 1

Particle behave likes wave is expanded on to the point it is distributed in space like a wave

Question 2

Trajectory of particles:

Answer 2

Imprecise and instead we have a wavefunction

Question 3

Wavefunction, Ψ

Answer 3

mathematical description of quantum system that varies with position.

Question 4

Ψ restrictions

Answer 4

Must be continues, always finite, differentiable and single valued.

Question 5

Time independent Schrodingers in 1 dimension.

Answer 5

-((ℏ^2)/2m) * d^2Ψ/dx^2 + V(x)Ψ = EΨ

Question 6

What does Ψ tell us?

Answer 6

Fuck all but ΨΨ* is the probability density

Question 7

Probability density integral:

Answer 7

∫ΨΨ*dx = 1, for one dimension

Question 8

hbar :ℏ =

Answer 8

h/2pi

Question 9

Hamiltonian operator, H =

Answer 9

LHS of schrodingers without Ψ

Question 10

Hamiltonian equation

Answer 10

HΨ =EΨ

Question 11

Schrodingers derivation

Answer 11

Ek +Ep = E
Ep = V(x)
Ek = p^2/2m, (p=mv)
p operator = ℏ/i *d.dx
Sub in and multiply by Ψ