PHYS-2020: General Physics IICourse Lecture NotesSection XDr. Donald G. LuttermoserEast Tennessee State UniversityEdition 3.3AbstractThese class notes are designed for use of the instructor and students of the course PHYS-2020:General Physics II taught by Dr. Donald Luttermoser at East Tennessee State University. Thesenotes make reference to the College Physics, 9th Edition (2012) textbook by Serway and Vuille.X. Interaction of Photons with MatterA. The Classical Point of View.1. A system is a collection of part icles that interact among them-selves via internal forces and that may interact with the worldoutside via external fields.a) To a classical physicist, a particle is an indivisible masspoint possessing a variety of physical properties that canbe measured.i) Intrinsi c Properties : These don’t depend onthe particle’s location, don’t evolve with time, andaren’t influenced by its physical environment (e.g.,rest mass and charge).ii) Extrinsic Properties: These evolve with timein response to the forces on the particle (e.g., posi-tion and momentum).b) These measurable quantities are called observables.c) Listing values of the observables of a particle at any time=⇒ specify its state. (A trajectory is an equivalent wayto specify a particle’s state.)d) The state of the system is just the collection of the statesof the particles comprising it.2. According to classical physics, all properties, intrinsic an d ex-trinsic, of a particle could be known to infi nite precision =⇒ forinstance, we could measure the precise value of both position andmomentum of a particle at the same time.X–1X–2 PHYS-2020: General Physics I I3. Classical physics predicts the outcome of a measu rement by cal-culating the trajectory (i.e., the values of its position and mo-mentum for all times after some initial (arbitrary) time t◦) of aparticle:{~r, ~p, t; t ≥ t◦} ≡ traject ory, (X-1)where the linear momentum is, by defin ition,~p ≡ m ~v , (X-2)with m the mass of the particle.a) Trajectories are state descriptors of Newtonian physics.b) To study the evolut ion of the state represented by thetrajectory in Eq . (X-1), we use N ewton’s Second L aw:ma = −∆PE∆r, (X-3)where PE is the potential energy of the particle.c) To obtain the trajectory for t > t◦, one only need to knowPE and the initial conditions =⇒ the values of ~r and ~pat the initial time t◦.d) Notice that classical physics tacitly assum es that we canmeasure the initial conditions without altering the motionof the particle =⇒ the scheme of classical physics is basedon precise speci fication of the position and momentum ofthe particle.4. From the discussion above, it can be seen that classical physicsdescribes a Determinate Universe =⇒ knowing the initial con-ditions of the constituents of any system, however complicated,we can use Newton’s Laws to predict the future.Donald G. Luttermoser, ETSU X–35. If th e Universe is determinate, then for every effect there is acause =⇒ the principle of ca usality.B. The Quantum Point of View.1. The concept of a particle doesn’t exist in the quantum world— so-called particles behave both as a particle and a wave =⇒wave-particle duality.a) The proper ties of quantum particles are not, in general,well-defined until they are measured .b) Unlike th e classical state, the quantum state is a conglom-eration of several possible outcomes of measur ements ofphysical pr operties.c) Quantum physics can tell you only t he pro bability th atyou will obtain one or another pr operty.d) An observer cann ot observe a microscopic system withoutaltering some of its properties =⇒ the interaction is un-avoidable : The effect of the observer cannot be reduced tozero, in principle or in practice.2. This is not just a matter of experimental uncertainties, natureitself will not allow position and momentum to be resolved to infi-nite precision =⇒ He isenberg Uncertainty Principle (HUP):∆x ∆px≥12h2π=¯h2, (X-4)where h = 6.62620 × 10−27erg-sec = 6.626 × 10−34J-sec isPlanck’s Cons tant.a) ∆x is the minimum uncertainty in the measurem ent ofthe position in t he x-direction at time t◦.X–4 PHYS-2020: General Physics I Ib) ∆pxis the minimum uncer tainty in the measurement ofthe momentum in the x-direction at time t◦.c) Similar constraints apply to the pairs of uncertainties ∆y,∆pyand ∆z, ∆pz.d) Position and momentum are fundamentally incompatibleobservab l e s =⇒ the Universe is inh erently uncertain!e) We can also write the HUP in terms of energy as∆E ∆t ≥¯h2. (X-5)f) This principle arises from geometry through a theoremknown as the Schwarz inequality of triang l e s . The d etailsof this relationship is too difficult to cover in this cou rse.It is covered in our sen ior-level Quantum Physics course.g) The HUP st rikes at the very heart of classical physics:the trajectory =⇒ if we cannot know the position andmomentum of a particle at t◦, we cannot specify the initialconditions of the particle and hence cannot calculate thetrajectory.h) Once we throw out trajectories, we can no longer use New-ton’s Laws, new physics must be invented!3. Since Newtonian (i.e., mechanics) and Maxwellian (i.e., thermo-dyn amics) physics describe the macroscopic world so well, physi-cists developing quantum m echanics demanded that when ap-plied to macroscopic systems, the new physics must reduce to theold physics =⇒ this Correspondence Principle was coined byNeils Bohr.Donald G. Luttermoser, ETSU X–54. Due to quantum mechanics probabilistic nature, only statisti-cal inf ormation about aggreg ates of identical systems can be ob-tained. Quantum mechanics can tell us nothing about the behav-ior of individual systems. Moreover , the statistical informationprovided by quantum theory is limited to the results of measure-ments =⇒ thou s hall not make any statements that can never beverified.5. In the realm of the very small, various quantities (i.e., energy,orbital angular momentum, spin angular momentum) are quan-tized =⇒ values of these parameters are not continuous, butinstead, come in “jumps” or steps.a) When we are in the realm of electr ons interacting withphotons (i.e., distances less than 10−9m), the laws ofquantum mechanics describe the physics.b) When we are in the realm of the nucleus (i.e., d istancesless than 10−14m), the laws of (nuclear) physics is de-scribed with quantum chromodynamics.6. Note that in this section of th e notes, we