- 12.1: Prelude to Quantum Mechanics
- The quantum-computer processor is the “brain” of a quantum computer that operates at near-absolute zero temperatures. Unlike a digital computer, which encodes information in binary digits (definite states of either zero or one), a quantum computer encodes information in quantum bits or qubits (mixed states of zero and one). Quantum computers are discussed in the first section of this chapter.
- 12.2: Wave functions
- In quantum mechanics, the state of a physical system is represented by a wave function. In Born’s interpretation, the square of the particle’s wave function represents the probability density of finding the particle around a specific location in space. Wave functions must first be normalized before using them to make predictions. The expectation value is the average value of a quantity that requires a wave function and an integration.
- 12.3: The Heisenberg Uncertainty Principle
- The Heisenberg uncertainty principle states that it is impossible to simultaneously measure the x-components of position and of momentum of a particle with an arbitrarily high precision. The product of experimental uncertainties is always larger than or equal to (frac{hbar}{2}). The energy-time uncertainty principle expresses the experimental observation that a quantum state that exists only for a short time cannot have a definite energy.
- 12.4: The Schrӧdinger Equation
- The Schrӧdinger equation is the fundamental equation of wave quantum mechanics. It allows us to make predictions about wave functions. When a particle moves in a time-independent potential, a solution of the time-dependent Schrӧdinger equation is a product of a time-independent wave function and a time-modulation factor. The Schrӧdinger equation can be applied to many physical situations.
- 12.5: The Quantum Particle in a Box
- In this section, we apply Schrӧdinger’s equation to a particle bound to a one-dimensional box. This special case provides lessons for understanding quantum mechanics in more complex systems. The energy of the particle is quantized as a consequence of a standing wave condition inside the box.
- 12.6: The Quantum Harmonic Oscillator
- The quantum harmonic oscillator is a model built in analogy with the model of a classical harmonic oscillator. It models the behavior of many physical systems, such as molecular vibrations or wave packets in quantum optics. The allowed energies of a quantum oscillator are discrete and evenly spaced. The energy spacing is equal to Planck’s energy quantum. The ground state energy is larger than zero. This means that, unlike a classical oscillator, a quantum oscillator is never at rest.
- 12.7: Quantum Tunneling of Particles through Potential Barriers
- A quantum particle that is incident on a potential barrier of a finite width and height may cross the barrier and appear on its other side. This phenomenon is called ‘quantum tunneling.’ It does not have a classical analog. The tunneling probability is a ratio of squared amplitudes of the wave past the barrier to the incident wave.
- 12.A: Quantum Mechanics (Answers)
- 12.E: Quantum Mechanics (Exercises)
- 12.S: Quantum Mechanics (Summary)
- Start studying Chemistry: Quantum mechanics. Learn vocabulary, terms, and more with flashcards, games, and other study tools.
- Covers some of the fundamental concepts of quantum mechanics. We have moved all content for this concept to for better organization. Please update your bookmarks accordingly.
- Chapter 11: Relativity & Chapter 12: Quantum Mechanics Overall Expectations: F1. Analyse, with reference to quantum mechanics and relativity, how the introduction of new conceptual models and theories can influence and/or change scientific thought, and lead to the development of new technologies.
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Covers some of the fundamental concepts of quantum mechanics. We have moved all content for this concept to for better organization. Please update your bookmarks accordingly.