PChem322 f20 w5

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Mon, Feb 22, 2021

Section 4.3 cont.

more about degeneracy...

- when a_x≠a_y≠a_z --> calculate energies

Degeneracy Excel worksheet

Section 4.4

Probability of finding particle in a certain area of a 1D box

Expectation Value problem

Weds, Feb 24, 2021

Review

Chapter 1

• Blackbody Radiation, Figure 1.2 with frequency axis (Sec 1.3)
• Photoelectric Effect, Figure 1.4 (Sec 1.4)
• Particle-Wave Duality (sec 1.5/1.6 - eq. 1.11)
• Emission Spectra/Rydberg Eq. (Sec 1.7 - eq. 1.13)

Chapter 2

• Properties of Waves (Sec 2.2)

- Standing wave derivation (eq. 2.10)

- construction/destruction of waves

- Classical Non-Dispersive Wave Equation (eq. 2.11)

• Derivation of Classical Non-Dispersive Wave Equation to QM Equivalent/time-dependent Schrodinger Eq. (Sec 2.3 - eq.2.21)
• Basics of Operator Algebra (operator, eignefunction, eigenvalue) (Sec 2.4)
• Orthogonal (eq. 2.31), Normalized (see ex prob 2.6), and complex conjugate. (Sec. 2.5)

Chapter 3

• Postulate 1 - wave function fully describes particle (sec 3.1)
• Postulate 2 - operators (sec 3.2)
• Postulate 3 - eignevalues (sec 3.3)
• Postulate 4 - Expectation Value (sec 3.4)

Chapter 4

• Particle in a 1D Box (Sec 4.2)

- boundary conditions

- acceptable wavefunction (eq. 4.13)

- normalization of wavefunction (eq. 4.15)

- energy (eq. 4.17)

• 2D/3D Boxes (Sec 4.3)

- 2D/3D wavefunctions

- 2D/3D energy

• Applying Postulates (Sec 4.4)

- Probability of finding particle in a region of box (Ex. Prob 4.3)

- Expectation Value (Ex. Prob. 4.4)

Chapter 5, partial (lab)

• A "real-life" 1D PIB - conjugated diene/polyene

- wavefuunction (same as 1D box)

- energy levels (calculated using 1D box energy)

- given a conjugated polyene

• determine molecular/box length (WebMO)
• considering the number of π-electrons, evaluate the "n" associated with the HOMO and LUMO.
• predict λ_max --> ΔE=hc/λ.
• given λ_max predict molecular length (ie. box length)

Additional Skills

Proficient with Excel

- basics of spreadsheets/graphing

- using global variable/universal constants

Proficient with Igor

- how to "load waves"

- graphing

- layout

::* Proficient with Mathematica

- Plot function

- Sin function

- Manipulate function

::* Proficient with WebMO

-starting jobs/drawing structures/submitting jobs/viewing results

Thurs, Feb 25, 2021

Exam 1 (Ch 1-5)