+2 or 3 more presentatios

Midterm I, Physics 274, Fall 2017 Average = 73 Low =24 High = 100 (2) For those doing well, keep up the good work and do not slack off (midterm, final and homework remain) Please talk to me if your score is below 50%

Announcements The four powerpoint lectures of Professor Pui Lam are now posted on the course web page. I greatly appreciate his efforts and will try to figure out some way to do some of the iclicker exercises he missed (many freebies !!). Next Midterm: Monday November 13th will cover waves as particles, particles as waves and quantum mechanics. (Hope there are no major conflicts with this date).

Quantum Mechanics V Quiz “The most incomprehensible thing about the world is that it is comprehensible.”– Albert Einstein Quiz Review of particle in a box

Q24.0 The name of this differential equation is: Einstein’s last equation deBroglie’s broken equation Space-independent Schroedinger Equation Time-independent Schroedinger Equation Bound-state Schroedinger’s Equation

Q24.0 The name of this differential equation is: Einstein’s last equation deBroglie’s broken equation Space-independent Schroedinger Equation Time-independent Schroedinger Equation Bound-state Schroedinger’s Equation Describes a free particle of mass m

Review: The Schrödinger equation in 1-D In a one-dimensional model, a quantum-mechanical particle is described by a wave function Ψ(x, t). [QM: remember point particles are waves] The one-dimensional Schrödinger equation for a free particle of mass m is The presence of i (the square root of –1) in the Schrödinger equation means that wave functions are always complex functions. The square of the absolute value of the wave function, |Ψ(x, t)|2, is called the probability distribution function. |Ψ(x, t)|2 dx tells us about the probability of finding the particle somewhere between location x and x+dx at time t . How do you calculate the total probability of finding the particle anywhere? Warning: |Ψ(x, t)|2 is not a probability, |Ψ(x, t)|2 dx is. 8

Q24.1 A solution to this differential equation is: A cos(kx) A e-kx A sin (kx) (B & C) (A & C)

Q24.1 A solution to this differential equation is: A cos(kx) A e-kx A sin (kx) (B & C) (A & C) Ans: E – Both (A) and (C) are solutions.

Q24.2 Condition on k just means that (p2)/2m = E. V=0, so E= KE = ½ mv2 = p2/2m The total energy of the electron is: Quantized according to En = (constant) x n2, n= 1,2, 3,… Quantized according to En = const. x (n) Quantized according to En = const. x (1/n2) Quantized according to some other condition but don’t know what it is. Not quantized, energy can take on any value.

Q24.2 …makes sense, because Condition on k is just saying that (p2)/2m = E. V=0, so E= KE = ½ mv2 = p2/2m The total energy of the electron is: Quantized according to En = (constant) x n2, n= 1,2, 3,… Quantized according to En = const. x (n) Quantized according to En = const. x (1/n2) Quantized according to some other condition but don’t know what it is. Not quantized, energy can take on any value. Ans: E - No boundary, energy can take on any value.

The possible energies of the free particle are quantized. Compare a free particle and a particle confined inside a box (“particle in a box”). According to quantum theory, which of the following statements is true? The possible energies of the free particle are quantized. The possible energies of the free particle and the particle in the box are quantized. Only the possible energies of the particle in the box are quantized. C 13

The possible energies of the free particle are quantized. Compare a free particle and a particle confined inside a box (“particle in a box”). According to quantum theory, which of the following statements is true? The possible energies of the free particle are quantized. The possible energies of the free particle and the particle in the box are quantized. Only the possible energies of the particle in the box are quantized. C 14

Review: Infinite Potential Well (“particle in a box”) E quantized by B. C.’s What is E? A. can be any value (not quantized). B. D. C. E. Screwy rep…. Energy vs. space..! Does this L dependence make sense?

Q25.1 C 16

Q25.1 Note n2 dependence C 17

Q25.2 Lambda = 2 L =C 18

What are the wavefunctions for the particle in the box ? Q25.2 Remember λ = 2 L =C Lambda = 2 L =C What are the wavefunctions for the particle in the box ? 19

Q25.3 Lambda = 2 L/n = 2(10^-10 m)/2= 10^-10 m A 20

Q25.3 Lambda = 2 L/n = (10^-10 m)/2= 0.5 x 10^-10 m B 21

Review: Infinite Potential Well (“particle in a box”) Probability of finding particle at a specific x-location? Probability of finding particle at a specific x-location? Screwy rep…. Energy vs. space..!

Infinite Potential Well (“particle in a box”) Screwy rep…. Energy vs. space..!

Infinite Potential Well (“particle in a box”) Probability of finding particle at a specific x-location? Screwy rep…. Energy vs. space..!