Welcome to Quantum Mechanics Jerry Gilfoyle Experimental Foundations 1 / 27
Welcome to Quantum Mechanics “The most important fundamental laws and facts have all been discovered, and these are so firmly established that the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote. ... Our future discoveries must be looked for in the sixth place of decimals.” Albert A. Michelson (1894) Jerry Gilfoyle Experimental Foundations 1 / 27
Welcome to Quantum Mechanics “The most important fundamental laws and facts have all been discovered, and these are so firmly established that the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote. ... Our future discoveries must be looked for in the sixth place of decimals.” Albert A. Michelson (1894) “I cannot seriously believe in the quantum theory...” Albert Einstein Jerry Gilfoyle Experimental Foundations 1 / 27
Welcome to Quantum Mechanics “The most important fundamental laws and facts have all been discovered, and these are so firmly established that the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote. ... Our future discoveries must be looked for in the sixth place of decimals.” Albert A. Michelson (1894) “I cannot seriously believe in the quantum theory...” Albert Einstein “The more success the quantum theory has the sillier it looks.” Albert Einstein Jerry Gilfoyle Experimental Foundations 1 / 27
The Physics 309 Approach 1 Start with a detector and take some data. My new detector. 2 Develop the quantum program. 3 Apply the quantum program. 4 What are the classical alternatives? Jerry Gilfoyle Experimental Foundations 2 / 27
The Spectral Lines Problem ← A toy atom. Jerry Gilfoyle Experimental Foundations 3 / 27
The Spectral Lines Problem ← A toy atom. − → Jerry Gilfoyle Experimental Foundations 3 / 27
Blackbody Radiation A black body is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or 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 radi- ated isotropically, independent of direc- tion. Jerry Gilfoyle Experimental Foundations 4 / 27
Measuring The Blackbody Radiation nm Frequency ( ν ) Wavelength ( λ ) Measured by Lummer and Pringsheim (1899). energy R T ( ν ) d ν = in the range ν → ν + d ν time-area Jerry Gilfoyle Experimental Foundations 5 / 27
The Ultraviolet Catastrophe Rayleigh-Jeans Law u ( ν ) d ν = 8 π c 3 k B T ν 2 d ν in the range ν → ν + d ν T - temperature. k B - Boltzmann constant. Jerry Gilfoyle Experimental Foundations 6 / 27
ϵ Planck’s Guess - the Boltzmann Distribution ϵ P ( ϵ ) Jerry Gilfoyle Experimental Foundations 7 / 27
ϵ Planck’s Guess - Do a Riemannian Sum ϵ P ( ϵ ) Jerry Gilfoyle Experimental Foundations 8 / 27
ϵ Planck’s Guess - Do a Riemannian Sum (low ν ) ϵ P ( ϵ ) Jerry Gilfoyle Experimental Foundations 9 / 27
ϵ Planck’s Guess - Do a Riemannian Sum (high ν ) ϵ P ( ϵ ) Jerry Gilfoyle Experimental Foundations 10 / 27
ϵ Planck’s Guess - Do a Riemannian Sum (high ν ) ϵ P ( ϵ ) Jerry Gilfoyle Experimental Foundations 11 / 27
ϵ Planck’s Guess - Do a Riemannian Sum (high ν ) ϵ P ( ϵ ) Jerry Gilfoyle Experimental Foundations 12 / 27
The Ultraviolet Catastrophe Rayleigh-Jeans Law u ( ν ) d ν = 8 π c 3 k B T ν 2 d ν in the range ν → ν + d ν T - temperature. k B - Boltzmann constant. Jerry Gilfoyle Experimental Foundations 13 / 27
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. Jerry Gilfoyle Experimental Foundations 14 / 27
The Blackbody Radiation COBE measurement of the cosmic microwave background radiation from J.C Mather et al. , Astrophysical Journal 354 , L37-40 (1990). Jerry Gilfoyle Experimental Foundations 15 / 27
The Photoelectric Effect Shine a light on metal and eject electrons. 1 Classical physics predicts that any fre- 2 quency/wavelength of light will work as long as the light is intense enough. Measurements by Lennard and others show very 3 different behavior including a linear dependence on frequency and a lower limit. No intensity dependence. Einstein uses Planck’s hypothesis to explain it 4 with a simple equation invoking the quantum hypothesis K max = eV stop = h ν − Φ where Φ is the work function, V stop is the mini- mum voltage for zero current, ν is the frequency of the light, and K max is the maximum kinetic energy of the ejected electrons. Jerry Gilfoyle Experimental Foundations 16 / 27
Uncertainty 1 In classical mechanics there is no limitation on the accuracy of our ability to measure the position � r ( t ) and velocity � v ( t ) of a particle. 2 The only limitations are experimental ones which can be overcome (hopefully) with improvements in technology and technique. 3 In wave mechanics (and quantum mechanics) this is no longer true! 4 For the motion of a quantum particle in one dimension the Heisenberg Uncertainty Principle is a fundamental limit that cannot be overcome. It is ∆ x ∆ p x ≥ � 2 where � = h / 2 π , h is Planck’s constant and the ∆’s are the uncertainties. Jerry Gilfoyle Experimental Foundations 17 / 27
A List of Mysteries (that Quanutm Mechanics Explained) Spectral lines Blackbody radiation Photoelectric effect Specific heat freeze-out Compton effect Davisson-Germer Radioactivity Atomic structure/nuclear physics The current list: https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_physics Jerry Gilfoyle Experimental Foundations 18 / 27
The Specific Heat Freezeout Problem Q = mc ∆ T = nC V ∆ T 2 H gas Jerry Gilfoyle Experimental Foundations 19 / 27
The Specific Heat 1 The Specific Heat Q = mc ∆ T = nC V ∆ T for gas in a fixed volume. 2 The Kinetic Model of Ideal Gases The gas consists of a large number of small, mobile particles and their 1 average separation is large. The particles obey Newton’s Laws, but can be described statistically. 2 The particles’ collisions are elastic. 3 The inter-particle forces are small until they collide. 4 Gas is pure. 5 Gas is in thermal equilibrium with the container walls. 6 3 C V = 1 2 N dof R where R is the gas constant. Jerry Gilfoyle Experimental Foundations 20 / 27
The Specific Heat 1 The Specific Heat Q = mc ∆ T = nC V ∆ T for gas in a fixed volume. 2 The Kinetic Model of Ideal Gases The gas consists of a large number of small, mobile particles and their 1 average separation is large. The particles obey Newton’s Laws, but can be described statistically. 2 The particles’ collisions are elastic. 3 The inter-particle forces are small until they collide. 4 Gas is pure. 5 Gas is in thermal equilibrium with the container walls. 6 3 C V = 1 2 N dof R where R is the gas constant. Monatomic gas: C V = 3 2 R . Diatomic gas: C V = 8 2 R = 4 R . Jerry Gilfoyle Experimental Foundations 20 / 27
Molar Specific Heat of Gases at Room Temperature 35 (J/K-mole) 30 SO 2 V CO C 2 H O CH 25 2 4 Cl 2 20 H N O CO 2 2 2 15 He Ar Ne Kr 10 5 0 Molecule Jerry Gilfoyle Experimental Foundations 21 / 27
Molar Specific Heat of Gases at Room Temperature 35 (J/K-mole) For gas in a fixed volume: SO 30 7 Q = mc ∆ T = nC V ∆ T 2 2 R V CO C 2 C V = 1 H O CH 25 2 4 2 N dof R Cl 2 5 2 R where R is the gas constant. 20 H N O CO 2 2 2 Monatomic gas: C V = 3 2 R . 15 3 2 R He Ar Ne Kr Diatomic gas: C V = 8 2 R = 4 R . 10 5 0 Molecule Jerry Gilfoyle Experimental Foundations 22 / 27
Moment of Inertia Depends on Axis of Rotation � � m i r 2 r 2 dm I = i → Jerry Gilfoyle Experimental Foundations 23 / 27
Moment of Inertia Depends on Axis of Rotation � � m i r 2 r 2 dm I = i → I x = I z >> I y Jerry Gilfoyle Experimental Foundations 23 / 27
Moment of Inertia Depends on Axis of Rotation � � m i r 2 r 2 dm I = i → I x = I z >> I y E rot = L 2 2 I Jerry Gilfoyle Experimental Foundations 23 / 27
Moment of Inertia Depends on Axis of Rotation � � m i r 2 r 2 dm I = i → I x = I z >> I y E rot = L 2 2 I E rot = l ( l + 1) � 2 2 I l = 0 , 1 , 2 , ... Jerry Gilfoyle Experimental Foundations 23 / 27
The Specific Heat Freeze-out of H 2 Q = mc ∆ T = nC V ∆ T 2 H gas Jerry Gilfoyle Experimental Foundations 24 / 27
Recall the Angular Momentum From Intro Physics and Classical Mechanics: L | = L = µ r 2 ˙ | � θ = µ r ( r ˙ θ ) = µ rv T = rp T = rp ⊥ � L = � r × � p y y p p φ p p = p || φ = 90 p = 0 r || θ r x x Jerry Gilfoyle Experimental Foundations 25 / 27
And the Moment of Inertia From Intro Physics and Classical Mechanics: � � m i r 2 r 2 dm I = i → Jerry Gilfoyle Experimental Foundations 26 / 27
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