Remember These? Carbon monoxide rigid rotator Zeeman effect in the - PowerPoint PPT Presentation

Remember These? Carbon monoxide rigid rotator Zeeman effect in the Sun Jerry Gilfoyle Radiation 1 / 13

Remember These? Carbon monoxide rigid rotator Zeeman effect in the Sun To explain these we invoked selection rules: ∆ l = ± 1, ∆ m = 0 , ± 1. Jerry Gilfoyle Radiation 1 / 13

Remember These? Carbon monoxide rigid rotator Zeeman effect in the Sun To explain these we invoked selection rules: ∆ l = ± 1, ∆ m = 0 , ± 1. WHY? WHY? WHY? Jerry Gilfoyle Radiation 1 / 13

The Question To explain the carbon monox- ide spectrum and the Zeeman effect we invoked angular mo- mentum selection rules: ∆ l = ± 1, ∆ m = 0 , ± 1 to under- stand light emission from the transitions between atomic en- ergy states. Where do these selections rules come from? Jerry Gilfoyle Radiation 2 / 13

What Is an Electromagnetic Wave? Jerry Gilfoyle Radiation 3 / 13

What Is an Electromagnetic Wave? 1 Consider a charge at a point in space. It creates an � E field at all points in space. Jerry Gilfoyle Radiation 3 / 13

What Is an Electromagnetic Wave? 1 Consider a charge at a point in space. It creates an � E field at all points in space. 2 Let the charge move and the � E field changes. Jerry Gilfoyle Radiation 3 / 13

What Is an Electromagnetic Wave? 1 Consider a charge at a point in space. It creates an � E field at all points in space. 2 Let the charge move and the � E field changes. 3 This disturbance of the � E propagates through space via electromagnetic induction - a changing electric field induces a changing magnetic field � B which induces an electric field... Jerry Gilfoyle Radiation 3 / 13

What Is an Electromagnetic Wave? 1 Consider a charge at a point in space. It creates an � E field at all points in space. 2 Let the charge move and the � E field changes. 3 This disturbance of the � E propagates through space via electromagnetic induction - a changing electric field induces a changing magnetic field � B which induces an electric field... 4 If the charge oscillates sinusoidally, then you get ‘typical’ electromagnetic (EM) waves. Jerry Gilfoyle Radiation 3 / 13

More on Oscillating Charges 1 How is the amplitude of the wave related to the oscillator? Jerry Gilfoyle Radiation 4 / 13

More on Oscillating Charges 1 How is the amplitude of the wave related to the oscillator? Amplitude oscillator ∝ Amplitude wave Jerry Gilfoyle Radiation 4 / 13

More on Oscillating Charges 1 How is the amplitude of the wave related to the oscillator? Amplitude oscillator ∝ Amplitude wave 2 What phenomenon connects points in space so the wave propagates? Jerry Gilfoyle Radiation 4 / 13

More on Oscillating Charges 1 How is the amplitude of the wave related to the oscillator? Amplitude oscillator ∝ Amplitude wave 2 What phenomenon connects points in space so the wave propagates? Electromagnetic induction Jerry Gilfoyle Radiation 4 / 13

More on Oscillating Charges 1 How is the amplitude of the wave related to the oscillator? Amplitude oscillator ∝ Amplitude wave 2 What phenomenon connects points in space so the wave propagates? Electromagnetic induction 3 Consider two charges ± e a distance r 0 Electric Field Lines apart and located along the z axis with dipole moment � d = e � r 0 . d = er 0 Jerry Gilfoyle Radiation 4 / 13

More on Oscillating Charges 1 How is the amplitude of the wave related to the oscillator? Amplitude oscillator ∝ Amplitude wave 2 What phenomenon connects points in space so the wave propagates? Electromagnetic induction 3 Consider two charges ± e a distance r 0 Electric Field Lines apart and located along the z axis with dipole moment � d = e � r 0 . 4 How is the electric field related to � � r 0 � and the dipole moment? d = er 0 Jerry Gilfoyle Radiation 4 / 13

More on Oscillating Charges 1 How is the amplitude of the wave related to the oscillator? Amplitude oscillator ∝ Amplitude wave 2 What phenomenon connects points in space so the wave propagates? Electromagnetic induction 3 Consider two charges ± e a distance r 0 Electric Field Lines apart and located along the z axis with dipole moment � d = e � r 0 . 4 How is the electric field related to � � r 0 � and the dipole moment? d = er � r 0 cos ω t = � 0 E ∝ � r 0 cos ω t → e � d cos ω t Jerry Gilfoyle Radiation 4 / 13

Energy Transfer in an Electromagnetic Wave S = 1 � � E × � B µ 0 Jerry Gilfoyle Radiation 5 / 13

〈 〈 〉 〉 Rapidly Oscillating Energy Transfer 1.0 0.5 E y ( N / C ) 0.0 - 0.5 - 1.0 0 5 10 15 20 t ( 10 - 9 s ) Jerry Gilfoyle Radiation 6 / 13

〈 〈 〉 〉 Rapidly Oscillating Energy Transfer 1.0 0.5 E y ( N / C ) 0.0 - 0.5 - 1.0 0 5 10 15 20 t ( 10 - 9 s ) 1.0 0.5 S x ( J / s - m 2 ) 0.0 - 0.5 - 1.0 0 5 10 15 20 t ( 10 - 9 s ) Jerry Gilfoyle Radiation 6 / 13

〈 〉 Rapidly Oscillating Energy Transfer 1.0 0.5 E y ( N / C ) 0.0 - 0.5 - 1.0 0 5 10 15 20 t ( 10 - 9 s ) 1.0 1.0 〈 S x 〉 = 1 / 2 0.5 0.5 S x ( J / s - m 2 ) S x ( J / s - m 2 ) 0.0 0.0 - 0.5 - 0.5 - 1.0 - 1.0 0 5 10 15 20 0 5 10 15 20 t ( 10 - 9 s ) t ( 10 - 9 s ) Jerry Gilfoyle Radiation 6 / 13

Rapidly Oscillating Energy Transfer 1.0 0.5 E y ( N / C ) 0.0 - 0.5 - 1.0 0 5 10 15 20 t ( 10 - 9 s ) 1.0 1.0 1.0 〈 S x 〉 = 1 / 2 〈 S x 〉 = 1 / 2 0.5 0.5 0.5 S x ( J / s - m 2 ) S x ( J / s - m 2 ) S x ( J / s - m 2 ) 0.0 0.0 0.0 - 0.5 - 0.5 - 0.5 - 1.0 - 1.0 - 1.0 0 0 5 5 10 10 15 15 20 20 0 5 10 15 20 t ( 10 - 9 s ) t ( 10 - 9 s ) t ( 10 - 9 s ) Jerry Gilfoyle Radiation 6 / 13

Time Dependence of Coefficients 1 2 | b P ( t ) t max ∼ 10 - 8 s 0.5 2 | a 0 t r , t ) | 2 = | ae iE n t / � | nlm � + be iE n ′ t / � | n ′ l ′ m ′ � | 2 P ( t ) = | Ψ( � Jerry Gilfoyle Radiation 7 / 13

Some Necessary Math Results Jerry Gilfoyle Radiation 8 / 13

Some Necessary Math Results Jerry Gilfoyle Radiation 9 / 13

Some Necessary Math Results Jerry Gilfoyle Radiation 10 / 13

Some Necessary Math Results Jerry Gilfoyle Radiation 11 / 13

Some More Necessary Math Results Jerry Gilfoyle Radiation 12 / 13

Some More Necessary Math Results Jerry Gilfoyle Radiation 13 / 13