Lets imagine that electrons are passing through a conducting wire. According to quantum mechanics , each electron is in form of wave function . Does that wave function have a value above 0 even outside that wire(even near 0), including the non conductive covering outside the conducting wire?If yes then , since there are billions of electrons flowing in that wire shouldnt some of them come out of that wire and shouldnt overall electrical energy change?
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To my best knowledge, the probability $|\psi(\vec{r},t)|$ of the electron to exist outside the conducting medium is defined by the potentials existing inside the medium and on its borders. Most models assume exponential decay of this probability. Otherwise, this problem is not trivial and has its own respected place in solid state physics. – MsTais Dec 18 '17 at 16:03