# Electron wavefunction

Is it true that electron wavefunction can be conceptualized as different periods the electron spends in all possible states, so when we interact with it it's more probable to find it in states in which it spends more time compared to states in which it spends less time just like unfair coin when it lands.

• Possibly forget about the concept of time spent and just consider the probability? With an unfair coin the "unfairness" is there at every instant of time. Commented Sep 22, 2023 at 9:06
• Commented Sep 22, 2023 at 11:36

A wave function of an electron distributed among several states is a superposition of the eigenfunctions corresponding to these states: $$\psi(x)=\sum_nc_n\phi_n(x).$$ The probability density of finding electron at point $$x$$ is then $$w(x)=|\psi(x)|^2=\sum_n\sum_m c_n c_m\phi_n^*(x)\phi_m(x)= \sum_n |c_n|^2|\phi_n(x)|^2 + \sum_n\sum_{m\neq n} c_n c_m\phi_n^*(x)\phi_m(x)$$ The suggested interpretation omits the second ("interference") term in the expression above, reducing QM to classical probability theory, where the uncertainty is only due to our ignorance of the state where electron is, but where otherwise it behave classically.