01 - Path Integrals in Quantum Mechanics 

The path integral is a slightly more advanced tool - and it becomes really useful when you go to quantum field theory - especially gauge theory. It may be better to pay more attention to the wave function and the operator algebra approach to qm at the beginning. That said, Mueller Kirsten's text book "Introduction to quantum mechanics" has a lot of nice details. Mosel's Path integrals in field theory is also nice - the initial chapters give a nice treatment for quantum mechanics.

Have you ever seen your watch going back in time? ;-)

@@jacobvandijk6525 Is not QM or Schrodinger's equation time reversal invariant? So, in principle given initial condition, evolution can also backward in time at least mathematically.

@@sumitdey365 Haha, mathematically a lot is possible. Just think of String Theory. But its practical relevance is almost zero.

Can you specify which integral you are referring to. Just a time stamp will do.

4:04 / 52:43 , on the left hand side you have two variables and on rhs you have in total four variables(x, x', ti, t) and you were integrating only over one variable that is dx' so you should be left three variables (x, ti, t) on left hand side of the equation.

But on the equation , the left hand side has two variables;

You are correct from a mathematical point of view. Psi(x,t) is being calculated from its initial value at t=ti, and as such it does depend on ti. However, in physics we do not usually supress this from the list of arguments, except when we are explicitly looking for dependence on initial conditions. This is similar to the fact that when we talk about the position of a point particle in 1 D, we write x(t),, and not x(t,ti). For a free particle for example we have x(t) = x0 + v0(t - ti) The ti is not usually included in the llist of arguments.

You are responsible for this atrocity! So, when everyone gets bored out of their minds - it will be your fault!

Sir, I am worried that you are saying it is my fault though it is your 3-4 hours hard work!😀

Unfortunately, there are none. These were written directly on a tablet, and I did not see any need to save the file then.