Project for which I need help using quantum mechanics but using schrodinger’s approach.
“Why we choose the unbounded condition and then we choose to bound it in the meanwhile as it wasn’t normalizable and we saw as it is plane waves we would have several disadvantages too like it's going left and right and why and then we went to infinite well and then it wasn’t realistic so we moved forward from those insights and then went to finite potential well and saw several things related to that and also after that and then we thought to go back for unbounded condition and then spectral decomposition for the wave packet and somehow localize it with that where we took linear superposition of the particular discrete solution and found it as a wave packet and then solved and there we found a lot loopholes even though we understood it’s somewhat realistic and then we went for different types of spectral decomposition and having generalized eigenstates for the continuous spectra of energy and the wave packet itself and then we bound it and solved rigorously and understood the mathematical insights and representations for each tiny study and insight and this is just for v(x)=0. And then from that we jump from solving that wave packets in unbounded and bounded conditions and knowing the insights from it through mathematical analysis and then do we think of some alternative to plane wave and that for through Fourier transformation we get relative amplitude and phases and that somehow dictates a generalized direction so do we solve the issue for that, after solving will get to know and then if that’s so then how exactly we have that specific shapes for discrete energy functions for the and compare the previous with the complex plane phases and amplitudes oscillations itself and how it moves in the complex plane and have that understanding. And finally have all the proofs of the above without gaps and having a clear intuitive understanding and moving forward to how to implement the Hilbert spaces and several operators itself with each and then think of for time dependent and then move forward to for V(x,t) as non zero for the project of including binary star systems for the simplest classical binary star system and then move forward in understanding and simulations and increase complexity.”