From the Udemy online course "The weird World of Quantum Physics - A primer on the conceptual foundations of Quantum Physics": https://www.udemy.com/quantum-physics/?couponCode=SLIDESHCOUPON

1. Max Planck
(1858-1947)
h=6.626×10−34 J/Hz
𝐸 𝑛 = 𝑛 ∙ ℎν
I. Hypothesis: Each mode has energy:
The Birth of Quantum Theory
n= 1, 2,3, …
𝐸1 = ℎ ν “Ground state energy”n=1
n=2
n=3
n=4
n=5
n=6
𝐸2 = ℎ (2 ∙ ν)
𝐸3 = ℎ (3 ∙ ν)
𝐸4 = ℎ (4 ∙ ν)
𝐸5 = ℎ (5 ∙ ν)
𝐸6 = ℎ (6 ∙ ν)𝜆/6
𝜆
𝜆/5
𝜆/4
𝜆/3
𝜆/2
From the Udemy online course: https://www.udemy.com/quantum-physics/?couponCode=SLIDESHCOUPON

2. Max Planck
(1858-1947)
h=6.626×10−34 J/Hz
𝐸 𝑛 = 𝑛 ∙ ℎν
Hydrogen’s and mercury’s spectral emission lines
(wavelength units: nm=10−9
m)
I. Hypothesis: Each mode has energy:
The Birth of Quantum Theory
n= 1, 2,3, …

3. II. Hypothesis:
the modes are not equally probable.
Boltzmann’s distribution law (much more modes
with lower energy than those with higher ones).
Ludwig Boltzmann
(1844-1906)
𝑃 𝐸 𝑛+1 < 𝑃 𝐸 𝑛
𝑃 𝐸∞ =0
𝐸1 + 𝐸2+ 𝐸3+...+ 𝐸∞< ∞ !
Max Planck
(1858-1947)
𝐸 𝑛 = 𝑛 ∙ ℎν
I. Hypothesis: Each mode has energy:
The Birth of Quantum Theory
h=6.626×10−34 J/Hz
n= 1, 2,3, …

4. Ultraviolet catastrophe
Intensity(a.u.)

5. Ultraviolet catastrophe
Rayleigh-Jeans formula
Planck‘s formula
Intensity(a.u.)

7. The cosmic microwave background radiation
Black body radiation can be explained only if we assume that:
Energy is absorbed or emitted only in discrete packets or ”quanta”.
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