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Page 1: Introduction to Course

• Overview of Course Structure

  • Includes 10 quizzes and 1 final exam

  • Topics covered: Quantum Mechanics, Thermodynamics, Newton/Maxwell/Classical Mechanics

• Lecture Topics

  • Potential Energy Diagram (3D)

  • Energy Status and Levels

  • Introduction to Quantum Mechanics

    • Particles and quantized energy levels

  • Wave Mechanics Overview

  • Measurement Techniques

    • Spectroscopy

    • Diffraction

• Emphasis on Theory over Equations

  • Chapter 9: Molecular Structure & Interaction

  • Chapter 11: Wave Mechanics

  • Quantum Mechanics Approach

    • Focuses on molecular levels and mathematical approximation

    • Limitations of the model but practical utility, including Bohr's model of quantizing energy states

    • Free energy vs. Quantized energy in confined systems

• Important Concepts

  • Planck's constant (h = 6.625 x 10^-34 J·s)

  • Relation to photons and oscillating atoms

  • Blackbody radiator relation to energy distribution

Page 2: Quantum Mechanics Fundamentals

• Key Quantum Mechanical Principles

  • Distribution and intensity comparison

  • Maxwell's Equations

  • de Broglie Hypothesis: ( p = mv = h/\lambda )

  • Heisenberg Uncertainty Principle: ( \Delta x \Delta p \geq \frac{\hbar}{2} )

• Wave Equation in Quantum Mechanics

  • Probability and bonding/orbitals

  • Energy state descriptions

    • Ground state and higher energy states defined via quantum numbers ( n )

    • Principle quantum numbers dictate energy levels

    • Energy state transitions involve absorption and release of energy

  • Angular momentum describes orbital shapes

    • Orbital quantum numbers: 0 (s), 1 (p), 2 (d), 3 (f)

    • Magnetic quantum numbers (

    • Spin quantum numbers

    • Each state defined uniquely by a set of 4 quantum numbers

  • Wave equations include terms for amplitude and relative phase

Page 3: Wave Mechanics and Solutions

• Wave Analysis

  • Amplitude (A) and coefficients in wave equations

  • Use of complex exponential functions to represent waves

  • Time-independent solutions in quantum chemistry: ( \Psi(x) = A e^{i(kx-wt)} )

• Energy Equations

  • Total energy representation via kinetic (KE) and potential energy (PE): ( E = KE + U )

  • Focus on the significance of total energy and its components ( (E - U) )

  • Relation to intensity observed in wave phenomena

  • 2nd Order Partial Differential Equations relevant to wave equations