Notes on notation, reading and HW.

You may have noticed that the notation we use in class and on the course blog sometimes differs from that used in the book Griffiths, Chapter 2. On your homework and exams I would like you to use the notation that I provide.

For the 1D harmonic oscillator (this week) we will emphasize the use of a length scale, \(a=(\hbar^2/mk)^{1/4}\) which depends on the strength of the potential, k, in units of \(eV/nm^2\). This let’s our wave-functions exhibit a simpler and more intuitive appearance. In our notation, k, m and \(\hbar\) are input parameters, and \(\omega_1\)is a frequency that emerges from solving the wave equation.

For our infinite square well (last week) we used a well that extends from -L/2 to L/2, so that it is centered at zero. In our treatment of the finite square well (soon) the well will also extend from -L/2 to L/2, so that all of our one-dimensional potentials: the harmonic oscillator, delta-function, infinite square-well and finite square-well, will be centered at zero. This will help us see relationships between these different systems (similarities and differences). It will also align well with our treatment of the 3D hydrogen atom, which uses pretty standard notation.

I think that the notation I provide will really help your learning of these 1D systems. I think that most or all of the HW problems you are given can be be done with the resources you have just from this blog and what we have done in class.