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Introduction to Quantum Mechanics

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Wavefunctions and the Born Interpretation

The wave-particle duality of matter is dealt with in quantum mechanics by considering that, rather than a particle traveling along a definite path, it is distributed through space like a wave.

Acceptable Forms of the Wavefunction

The Born interpretation means that many wavefunctions which would be acceptable mathematical solutions of the Schrodinger equation are not acceptable because of their implications for the physical properties of the system.

The One-Dimensional Schrodinger Equation

The Schrodinger equation is an equation for finding the wavefunction of a system. There are two basic forms of the equation, a time-dependent form that gives the time-dependent wavefunction (showing how properties of the system change with position and time), and a time-independent form that gives the time-independent wavefunction, showing how properties of the system depend upon position, but not how they change over time.

Principles of Quantum Mechanics

Before a detailed study of quantum mechanics, it is worth introducing some of the mathematical terms and concepts that will feature heavily in this area, and may otherwise be new or unfamiliar.

The Bohr Model of Hydrogenic atoms

This model was created by Nils Bohr to explain the form of the emission spectrum of atomic hydrogen, which consists of series of discrete lines.

Wave-Particle Duality

A fundamental distinction was drawn in classical physics between waves and particles. This was refuted by experimental evidence that showed waves demonstrating particle-like character and vice versa.

Further breakdowns of Classical Physics

Atomic and Molecular Spectra. Some of the most impressive evidence for non-classical behaviour comes from the spectra of atoms and molecules. Rather than showing emission or absorption of radiation at all frequencies, nonzero intensities are only observed at discrete frequency value

Black body radiation and the Planck distribution

In the late nineteenth and early twentieth centuries, a great deal of experimental evidence began to accumulate for which classical mechanics could provide no explanation. It was the consideration and explanation of these data which led to the development of quantum mechanics.