1000 Solved Problems in Modern Physics

(Romina) #1

Chapter 2


Quantum Mechanics – I


2.1 Basic Concepts and Formulae


Wave number


ν ̃=

1

λ

(2.1)

1fm= 10 −^15 m; 1A ̊ = 10 −^10 m; 1 nm = 10 −^9 m; 1μm = 10 −^6 m;c =
197 .3Mev−fm


Photon energy


E=hv (2.2)

Photon momentum


p=hν/c

Photon energy−wavelength conversion


λ(nm)=

1241

E(eν)

(2.3)

de Broglie wavelength


λ=h/p (2.4)

λ(electron) :λ(A) ̊ =(150/V)^1 /^2 (2.5)
λ(neutron) :λ(A) ̊ = 0. 286 E−^1 /^2 (Ein ev) (2.6)

Atomic units


The Bohr radius^2 /mee^2 is frequently used as the unit of length in atomic physics.
In atomic units the energy is measured in multiples of the ionization energy of
hydrogen atom that ismee^4 / 2 ^2. In these units^2 =1,e^2 =2 andme =^12 in
all equations.


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