Quantum Mechanics Unit IV Quiz

Quantum Mechanics (Unit IV)

• Students should read Chapter 15 ("Development of Quantum Mechanics") and Chapter 16 ("Quantum Mechanics") from Engineering Physics, Second Edition (H.K. Malik & A.K. Singh).
• Both chapters are required reading.

Why Quantum Mechanics

• Classical mechanics failed to explain certain phenomena (e.g., blackbody radiation, photoelectric effect)
• A new theory, quantum mechanics, was developed to address these failures.

Classical Mechanics - A Brief History

• Classical mechanics includes concepts like Newton's Laws of Motion and theories developed by Euler, Lagrange, and Hamilton.
• Fundamental constants are included (e.g., gravitational constant G, acceleration due to gravity g).

Classical Electrodynamics

• Key figures in classical electrodynamics are highlighted (Coulomb, Ampere, Faraday, Lorentz, Maxwell). (names and dates included but not in bullet points)
• Mathematical equations or formulas are presented, but not included in bullet points (e.g., those for electric and magnetic fields).

Experiments and Ideas Prior to Quantum Theory (Before 1913)

• This section focuses on experiments and theories prior to the development of full quantum theory.

Blackbody Radiation and Quanta of Energy

• The failure of classical physics in explaining blackbody radiation is discussed.
• Rayleigh-Jeans Law is introduced, as part of classical physics
• This theoretical model had significant errors in predicting results against experimental data.

Planck

• Max Planck's work (1858-1947) in blackbody radiation is detailed.

• Planck introduced the idea of energy quanta.

• Energy is quantized at discrete values.

Failure of Classical Theory 1

• Classical physics predicted a "UV catastrophe" regarding blackbody radiation: infinite energy at high frequencies.
• Planck resolved this issue by introducing the concept of quantized energy.

Radiation Interaction with Matter: Photoelectric Effect and Quanta of Light

• Photoelectric effect observations are described

Photoelectric Effect

• Albert Einstein's (1905) explanation of the photoelectric effect, and its implications
• Millikan's experimental verification of Einstein's work.
• Photoelectric effect and the role of light intensity: intensity affects the number of ejected electrons; frequency sets a minimum intensity value

Failure of Classical Theory 2

• Classical physics could not explain why red light couldn't cause the photoelectric effect in certain materials

Atomic Structure

• Introduction to atomic structure models.

Nuclear Atom Model (1911): Ernest Rutherford

• Rutherford's experiment and model of the atom, introducing the concept of the atomic nucleus

Failure of Classical Theory 3

• Classical electrodynamics predicted that an accelerating charged particle, such as an electron orbiting the nucleus, would lose energy, and thus fall into the nucleus.
• This issue pointed to the inadequacies of classical physics.

Atomic Spectra

• Spectroscopy and the concept of discrete lines
• Rydberg formula applications in spectroscopy (formulas are in the notes)

Old Quantum Theory (1913 - 1924)

• Bohr's model of atomic structure

The Wave Function, ψ

• De Broglie's concept of wave-like nature of particles
• The wave function (Ψ) as the fundamental concept in quantum mechanics.

First Postulate of Quantum Mechanics

• A physically realizable state, represented by a wave function, holds all the system's information.

Second Postulate of Quantum Mechanics

• Probability density of a particle being found in a specific volume at a given time (formula included)

Third Postulate of Quantum Mechanics

• Observables (e.g., position, momentum, energy) are associated with operators, enabling their measurement within the quantum model. (Formulas included)

Fourth Postulate of Quantum Mechanics

• Schrödinger equation describing the evolution of a quantum mechanical system. (Equation included)

Non-Relativistic Schrödinger Equation

• Time-independent and time-dependent versions presented (formulas shown)

Particle in a Box

• Quantum mechanical calculation of particle energy limitation to a box
• Derivation of energy quantum (formula shown)

Quantized Energy

• The energy levels of a particle in a box are quantized; energies are proportional to the square of the quantum number (n)

Quantum Tunnelling

• Wave functions can pass through potential barriers. The transmission probability depends on the barrier's height and width (mathematical formulas in notes)

Applications of Quantum Tunnelling

• Nuclear fusion, electronics, and quantum biology.

Wave-Particle Duality

• Wave properties of particles and particle properties of waves.

Heisenberg Uncertainty Principle

• The act of measuring a particle disturbs it, imposing inherent limits on the precision with which certain pairs of quantities (like position and momentum) can be known. (Formula shown)

Phase Velocity and Group Velocity

• Velocity at which the phase and the overall amplitude of a wave propagates in a medium (mathematical formulas included)

This quiz covers Chapters 15 and 16 from Engineering Physics focusing on the development of quantum mechanics and its significance. Students will explore the limitations of classical mechanics and the foundational concepts in classical electrodynamics.