In quantum field theory (QFT), the wave function of an electron does not represent the probability of finding an electron, but rather the intensity or amplitude of the electron field at a given point in spacetime.
In QFT, particles such as electrons are described by quantum fields that permeate all of spacetime. These fields are operators that act on a mathematical framework known as a Fock space, which describes the quantum states of the particles.
The wave function, or more precisely the field configuration, associated with an electron field is a complex-valued quantity defined at each point in spacetime. It represents the amplitude or intensity of the electron field at that point. The square of the absolute value of the wave function gives the probability density of finding a particle at that point, but it does not represent the probability of finding an electron itself.
The interpretation of the wave function in quantum mechanics, where it represents the probability amplitude of finding a particle at a given location, is different from the interpretation in QFT. In QFT, the wave function of a particle field is more closely associated with the amplitude of the underlying field itself, rather than the probability of finding a particle.
In QFT, particles are understood as excitations or quanta of their respective fields. The probability of finding a particle is determined by the field's state, which is described by a more complex mathematical object called the quantum state or state vector. The quantum state encompasses the information about the probabilities of different field configurations and the creation or annihilation of particles.
It is important to note that the formalism and interpretation of QFT can be quite different from non-relativistic quantum mechanics, where the wave function typically describes the probability distribution of finding a particle at a given position. In QFT, the focus is on the dynamics of fields and their interactions, and the wave function represents the intensity or amplitude of the underlying field rather than the probability of finding a particle.