Bohr, Heisenberg, and others tried to explain what these experimental results and mathematical models really mean. The term Copenhagen interpretation has been applied to their views in retrospect, glossing over differences among them. While no definitive statement of "the" Copenhagen interpretation exists, the following ideas are widely seen as characteristic of it.
# A system is completely described by a quantum state (Heisenberg)
# How the quantum state changes over time is given by a wave equation, the Schrödinger equation imparting wave characteristics to light and matter.
# Atomic interactions are discontinuous. (Planck's quantum of action)
# The description of nature is essentially probabilistic. The probability of an event—for example, where on the screen a particle shows up in the double-slit experiment—is related to the square of the absolute value of the amplitude of its wave function. (Born rule, due to Max Born, which gives a physical meaning to the wave function in the Copenhagen interpretation: the probability amplitude)
# The values of incompatible pairs of properties of the system cannot be known at the same time. (Heisenberg's uncertainty principle)
# Matter, like light, 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)
# Measuring devices are essentially classical devices and measure classical properties such as position and momentum.
# The quantum mechanical description of large systems should closely approximate the classical description. (Correspondence principle of Bohr and Heisenberg)