Introduction To Quantum Mechanics - Copenhagen Interpretation

Copenhagen Interpretation

Bohr, Heisenberg and others tried to explain what these experimental results and mathematical models really mean. Their description, known as the Copenhagen interpretation of quantum mechanics, aimed to describe the nature of reality that was being probed by the measurements and described by the mathematical formulations of quantum mechanics.

The main principles of the Copenhagen interpretation are:

1. A system is completely described by a wave function, . (Heisenberg)
2. How changes over time is given by the Schrödinger equation.
3. The description of nature is essentially probabilistic. The probability of an event — for example, where on the screen a particle will show up in the two slit experiment — is related to the square of the amplitude of its wave function. (Born rule, due to Max Born, which gives a physical meaning to the wavefunction in the Copenhagen interpretation: the probability amplitude)
4. It is not possible to know the values of all of the properties of the system at the same time; those properties that are not known with precision must be described by probabilities. (Heisenberg's uncertainty principle)
5. Matter, like energy, exhibits a wave-particle duality. An experiment can demonstrate the particle-like properties of matter, or its wave-like properties; but not both at the same time. (Complementarity principle due to Bohr)
6. Measuring devices are essentially classical devices, and measure classical properties such as position and momentum.
7. The quantum mechanical description of large systems should closely approximate the classical description. (Correspondence principle of Bohr and Heisenberg)

Various consequences of these principles are discussed in more detail in the following subsections.