Atomic and Molecular Physics FYSC11 HT 2014

From: Demtröder, Atoms, Molecules and Photons

Spherical harmonics

From

: Dem

tröde

r, A

tom

s, M

olec

ules

and

Pho

tons

Polar diagrams of spherical harmonics

From: Demtröder, Atoms, Molecules and Photons

Spherical harmonics Angular parts of orbital wave functions = linear combinations of spherical harmonics

Angular parts of orbital wave functions = linear combinations of spherical harmonics

Contour plots of 3d orbitals of hydrogen

B. Averill and P. Eldredge, General Chemistry: Principles, Patterns, and Applications

Q13: Orthogonality of hydrogen wave functions

Consider the following statement: The orthogonality of two wave functions φnlm and φn’l’m’ implies that at any point of space φn’l’m’ has to be zero in this point if φnlm is different from zero in this point and vice versa. A. Correct. B. Incorrect.

Which properties do you expect for the probabilities of finding the electron at a distance r from the nucleus (and

therefore for the wave functions) for different different n and l?

The effective potential of the hydrogen atom

The minimum of the effective potential as a function of l

Radial wave functions of the hydrogen atom

From: Thorne, Litzén, Johansson, Spectrophysics

From: Demtröder, Atoms, Molecules and Photons

Q14: Radial probabilities

The probability of finding the electron at a distance from the proton between r and r+dr is given by A. B. C.

From: Thorne, Litzén, Johansson, Spectrophysics

Hydrogen atom, radial probability densities

From: Atom- och molekylfysik, kompendium Uppsala universitet

From: Haken and Wolf, The Physics of Atoms and Quanta

Hydrogen atom, density distributions

What are your expectations for the wavefunctions of Li2+ in comparison to those of hydrogen? A. The wave functions are contracted. B. The wave functions are the same. C. The wave functions are expanded.

Q15: Lithium ion wave functions

Hydrogen and lithium2+, radial probability densities