PHYS 041C Lecture Notes - Lecture 2: Reflection Coefficient, Probability Amplitude, Delta Potential
Document Summary
This may be something you think you now understand or something that you still don"t understand after reading the book. The derivations seem dense and extremely difficult to follow, it gets in the way of actually understanding the physics. The double well potential was hard to follow, and it took several re-reads to finally understand the concept. For a dirac delta potential well, the wavefunction does not have to be completely continuous (in other words, smooth), but it must be continuous and piecewise as seen in figure 4. 15. Since it"s piecewise and simultaneously continuous, its derivative is not finite. We know this to be true since (x) is normalizable (in other words, the probability amplitude is a real, finite value) and approaches zero as |x| approaches infinity. The gse for a double delta function potential well is less than the gse for a single delta function potential well due to the eigenvalue requirement that corresponds to the less-than energy.
