Welcome to Quantum Mechanics I cannot seriously believe in the - - PowerPoint PPT Presentation

Experimental Foundations

Welcome to Quantum Mechanics

“I cannot seriously believe in the quantum theory...” Albert Einstein

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Experimental Foundations

Welcome to Quantum Mechanics

“I cannot seriously believe in the quantum theory...” Albert Einstein “The more success the quantum theory has the sillier it looks.” Albert Einstein

– p. 1/1

Experimental Foundations

Welcome to Quantum Mechanics

“I cannot seriously believe in the quantum theory...” Albert Einstein “The more success the quantum theory has the sillier it looks.” Albert Einstein

– p. 1/1

Experimental Foundations

The Spectral Lines Problem

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Experimental Foundations

The Spectral Lines Problem

− →

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Experimental Foundations

The Spectral Lines Problem

− → − →

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Experimental Foundations

A ‘Simple’ Example - Infinite Rectangular Well Potential

a x V(x)

V (x) = 0 < x < a = ∞ x ≤ 0 and x ≥ a |n =

• 2

a sin nπx a

• En = n2 2π2

2ma2

1 2 3 4 5 6 7 8 9 10

Energy Energy Levels n

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Experimental Foundations

Blackbody Radiation

A black body is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency

• r angle of incidence. In thermal equilibrium (at a constant

temperature) it emits electromagnetic radiation called black-body radiation with two notable properties.

• 1. It is an ideal emitter: it emits as

much or more energy at every frequency than any other body at the same temperature.

• 2. It is a diffuse emitter: the energy

is radiated isotropically, indepen- dent of direction.

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Experimental Foundations

Measuring The Blackbody Radiation

Frequency

Visible light λ ≈ 400 − 700 nm

Measured by Lummer and Pringsheim (1899).

RT (ν)dν =

energy time-area in the range ν → ν + dν

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Experimental Foundations

The Ultraviolet Catastrophe

Rayleigh-Jeans Law

u(ν)dν = 8π c3 kBTν2dν

in the range ν → ν + dν

T - temperature. kB - Boltzmann constant.

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Experimental Foundations

Planck’s Guess - the Boltzmann Distribution

For ν → ν + dν

∆ǫ → 0

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Experimental Foundations

Planck’s Guess - Do a Riemannian Sum

For ν → ν + dν

∆ǫ = 0 for small ν

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Experimental Foundations

Planck’s Guess - Do a Riemannian Sum, low ν

For ν → ν + dν

∆ǫ = hν for small ν

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Experimental Foundations

Planck’s Guess - Do a Riemannian Sum - not as low

For ν → ν + dν

∆ǫ = hν for not as small ν

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Experimental Foundations

Planck’s Guess - Do a Riemannian Sum - moderate

For ν → ν + dν

∆ǫ = hν for moderate ν

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Experimental Foundations

Planck’s Guess - Do a Riemannian Sum - high ν

For ν → ν + dν

∆ǫ = hν for high ν

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Experimental Foundations

Planck’s Guess - Do a Riemannian Sum - higher ν

For ν → ν + dν

∆ǫ = hν for higher ν

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Experimental Foundations

The Ultraviolet Catastrophe

Rayleigh-Jeans Law

u(ν)dν = 8π c3 kTν2dν

in the range ν → ν + dν

T - temperature. k - Boltzmann constant.

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Experimental Foundations

The Blackbody Radiation

Scan of first showing of the COBE measurement of cosmic microwave background radiation at the American Astronomical Society meeting in January, 1990.

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Experimental Foundations

The Blackbody Radiation

COBE measurement of the cosmic microwave background radiation from J.C Mather et al., Astrophysical Journal 354, L37-40 (1990).

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Experimental Foundations

Other Mysteries That Needed Quantum Mechanics

Photoelectric effect Compton effect Spectroscopy Davisson-Germer Radioactivity Nuclear sizes

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