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Extra info for Introduction to QFT (Quantum Mech. IV lecture notes, CMU)
Sample text
Cold electron emission This phenomenon is observed when a strong electric field is directed towards the surface of a metal, resulting in the emission of electrons. This occurs even if the electrons are not thermally excited (which would be thermionic emission) and so do not have enough energy to escape classically. 5(b)), when the electrons are confined within the metal by an energy barrier formed by the work function (see the discussion of the photoelectric effect in chapter 1). When the electric field is applied, the potential is changed, so that at a short distance from the surface of the metal the potential energy is less than the energy of the electrons inside the metal.
Hint: Make the substitution y = −x and show first that u(x) = Au(−x) where A is a constant. 6 Consider a particle of mass m subject to the one-dimensional potential V (x) that is given by V =0 if − a V = V0 if a < |x| x a or if |x| > b b where b > a. Write down the form of an even-parity solution to the Schr¨odinger equation in each region in the case where E < V0 . Note that the particle is not bound in this potential as there is always a probability of quantum-mechanical tunnelling, so solutions exist for all values of E.
This occurs even if the electrons are not thermally excited (which would be thermionic emission) and so do not have enough energy to escape classically. 5(b)), when the electrons are confined within the metal by an energy barrier formed by the work function (see the discussion of the photoelectric effect in chapter 1). When the electric field is applied, the potential is changed, so that at a short distance from the surface of the metal the potential energy is less than the energy of the electrons inside the metal.