Quantum Mechanics
(or Wave Mechanics)
The General Features of Quantum Mechanics:
- Linearity
- Nessecity of complex numbers
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- Loss of determinism
- Superposition
- Entanglement
The Bohr model of the atom allowed physicists to understand the organization of energy levels. However, it was far from a complete theory. One shortcoming was that it did not explain why some spectral lines are stronger than others. More fundamentally, it was an ad hoc theory. Bohr had no explanation of why stationary states exist, or why angular momentum must be quantized in some particular way. These were just postulates. A much deeper understanding was needed.
An important step was made by Louis de Broglie, who proposed the revolutionary idea that if light could exhibit a wave–particle duality, then maybe all matter could. That is, an electron orbiting a nucleus has certain wavelike properties, and it is those properties that determine the states that are stable. One could think of the electron as having a certain wavelength. Stationary states could be those whose circumference contained an integral number of wavelengths, producing a pattern that reinforced during each orbit (like a standing wave). It was necessary to have expressions for the wavelength and frequency of a particle, and de Broglie noted that if the wavelength was taken as h/p (where p is the momentum of the particle) and the frequency as E/h, then the orbits allowed by the standing wave idea were the same as the orbits that Bohr found from his postulates.
This is clearly a departure from the normal way of looking at matter.
The picture as presented by Bohr and de Broglie is quantum theory in its most naive form. It was realized that if particles behave, in some fashion, like waves then the description of particle motions (mechanics) must be changed from Newton’s laws of motion to laws of motion involving waves. (Of course, in the limit of large objects, these new laws of motion must reduce to Newton’s laws, because Newton’s laws work quite well for large objects.) Theories that describe the mechanics of waves are or quantum mechanics.
One such theory was presented in 1925 by Erwin Schrödinger. In his theory the information about the motion of a particle is contained in a wave function. Schrödinger’s interpretation of the wave function was that it is related to the probability of finding a particle in a particular place with a particular momentum. This replaced the absolute determinism of classical physics, with the statement that we can only predict where a particle is likely to be, but not exactly where it will be. However, we can predict the average positions and momenta of a large group of particles, and it is these average properties that we see (and measure) in our everyday world.
Many physicists (including Einstein) were not comfortable with this probabilistic interpretation, but quantum theory has been very successful in predicting the outcome of a wide variety of experiments.