Wave-packet states. Tuesday class.

A wave-packet refers to a method for the creation of a single electron state using many single-electron energy eigenstate wave-functions together.
We will discuss this tomorrow on Tuesday April 30, in class. A wave packet state can be viewed as part of a natural extension of the progression from electron states involving a single energy-eigenstate wave function, to non-stationary states involving 2 energy-eigenstate wave-functions (as in problems 6, 8&9 from HW4, problem 6 from HW2, problem 5 from HW1 and problem 4 from midterm 1) to wave-packets involving an infinite number of energy eigenstate wave-functions.

The concept from linear algebra (Hilbert space theory) that the energy eigenstates form a "basis" in which one can write any general state and wave-function underlies all this.
(The eigenstates of a Hermitian matrix can be chosen in such a manner that they form an orthonormal basis...  Is this familiar?  This encompasses concepts like spanning, completeness, linear independence, inner products and all that. The word operator can be substituted for matrix. Sometimes self-adjoint subs in for Hermitian, We view the Hamiltonian as Hermitian, because it is, and the Schrodinger equations as self-adjoint. The energy eigenstates form a basis in which any state can be "expanded". That is, represented as a linear combination or, equivalently, a superposition. This is a very powerful, useful and important thing.