My ramblings – part one

I woke up this morning and just randomly opened a chapter in the quantum mechanics book. I could see all those paragraphs, some underlined, things written here and there. “Yes I’ve been here before”, I thought. I don’t really wanted to read but then I started reading unwillingly. Questions started popping in my head. Its like when you read a thing but when you come back to it after a long time, you ask something to yourself and then the whole paragraph makes sense, like why it was written in the first place. “Oh, so that’s what it was trying to say!”. Now you understand that thing because you asked the right question in your mind. And you were curious to know why. The answers were just sitting there (like all of the truth) but what was missing is the right question.

And that right question was, “How do you solve a time dependent schroedinger equation?”. I have only focused on how the time independent one is solved that I forgot why we were doing it in the first place. You get different solutions for different energy values, so called infinite solutions. But then you can always form a linear combination of all of them to get the more general solution, or the solution of time dependent shroedinger equation.

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My ramblings – part two

In mechanics, finding x and t is just the beginning. After that we have velocity, acceleration, force etc. to calculate. But calculating psi in quantum is such a difficult task.

In mechanics there are so many situations you have to apply those formulas to. But in quantum mechanics its so hard to even get past the first step. It’s just one of the many problems during qm learning process.

And another thing that’s even more daunting is that, the whole edifice of QM is based on the Hamiltonian formulation of classical mechanics (whatever that means 😕).

Probably because QM is so hyped of being mysterious and fundamental; that’s why there is an awe when we read these things, even if it’s hard. But in that sense, mechanics or statistical mechanics is as much mysterious and fundamental. But it still doesn’t feel that way (to me). I don’t know why.