schrodinger wave equation and the hydrogen atom

del squared

h bar

schrodinger wave equation in words and symbols

dimensions and time dependency for schrodinger equation

3 dimensional, time-independent

wavefunction symbol and variation

ψ (psi)

varies with position (x, y, z) and contains information on the properties and behaviour of a particle but is not directly measurable

when can the schrodinger equation be solved

only for two-body problems ie nucleus and a single electron (H, He⁺, Li²⁺)

born interpretation

ψ² (referred to as electron density) is proportional to the probability of finding the particle in a small volume dV

heisenberg uncertainty principle

the wave properties of matter mean it is impossible to know precisely the position and momentum of electrons simultaneously - hence quantum mechanics considers the probability of finding electrons within certain volumes.

see photos

E_n for the hydrogen atom from Schrodinger?

matches predictions of Rydberg and Bohr (that it is dependent on principle quantum number n)

values of n, l and m_l from schrodinger

values of l for spdf

polar coordinates

• number of dimensions

• diagram

• how to convert between cartesian and polar

x = rcosθ

y = rsinθ

spherical coordinates

• why are they called spherical

• number of dimensions

• diagram

• how to convert between cartesian and spherical

atoms are spherical so spherical polar coordinates are used