Me watching this only halfway through my algebra class. I’m just mesmerized by math at this point and love seeing how far/advanced math gets and the different kinds of math. It’s really cool.
I have seen the video of 28 and 29. There are problems. In this two section try to prove dN/dt=0. The condition is psi(x,t) is 0 at infinity. and d psi(x,t)/dt is bounded. This condition is is not enough. psi(x,t) is 0 at infinity is not enough. Assume psi(x,t) is proportion to 1/r, here r is distance from origin to the field point. Then psi(x,t) is 0 at infinity, but the integral along the surface to psi(x,t) is not 0. Even this surface is a sphere with its radius infinity. Hence, psi(x,t) close to 0 faster than 1/r, at r -> infinity.
Yes, you are correct. In fact, if we consider the condition that the integral of the probability density has a finite value, you will find that ψ had better converge to zero with an order of of 1/r^(1.5+δ).
The current in the lecture is actually current density, so it is probability per unit time per unit area. The area(2 dimensional) is actually the area perpendicular to the current flow, so it only works in 3D. In 2D, current density is probability per unit time per unit length because the current is flowing perpendicular to a length(1 dimensional). In 1D, it is probability per unit time because the current is flowing perpendicular to 0 dimensions.
The polydynamics of the movement generates pseudo-autonomy as material property, of the autogenous phenomenon; existing.(...) Simultaneous as my unidimensional variability... unidimensional variability = live-beings
I have seen the video of 28 and 29. There are problems. In this two section try to prove dN/dt=0. The condition is psi(x,t) is 0 at infinity. and d psi(x,t)/dt is bounded. This condition is is not enough. psi(x,t) is 0 at infinity is not enough. Assume psi(x,t) is proportion to 1/r, here r is distance from origin to the field point. Then psi(x,t) is 0 at infinity, but the integral along the surface to psi(x,t) is not 0. Even this surface is a sphere with its radius infinity. Hence, psi(x,t) close to 0 faster than 1/r, at r -> infinity.
Here are the solutions to Problem Set #2. I do not guarantee their correctness. Please edit, comment and correct. docs.google.com/document/d/1M1Z4EVFY25RjeSOqw-iTt3ln_eFD9eU-zErn52mzEek/edit?usp=sharing
This guy is a really clear instructor. Nicely done.
Me watching this only halfway through my algebra class. I’m just mesmerized by math at this point and love seeing how far/advanced math gets and the different kinds of math. It’s really cool.
So from now on, when you see the level of water in your bathtub going down just think of it as a decreasing probabililty that you will drown in it.
I have seen the video of 28 and 29. There are problems. In this two section try to prove dN/dt=0. The condition is psi(x,t) is 0 at infinity. and d psi(x,t)/dt is bounded. This condition is is not enough. psi(x,t) is 0 at infinity is not enough. Assume psi(x,t) is proportion to 1/r, here r is distance from origin to the field point. Then psi(x,t) is 0 at infinity, but the integral along the surface to psi(x,t) is not 0. Even this surface is a sphere with its radius infinity.
Hence, psi(x,t) close to 0 faster than 1/r, at r -> infinity.
Those conditions are for 1d
Yes, you are correct. In fact, if we consider the condition that the integral of the probability density has a finite value, you will find that ψ had better converge to zero with an order of of 1/r^(1.5+δ).
In my country Gauss' law is Green-Ostrogradski theorem.
In physics it's called Gauss Law and in mathematics it's called Gren-Ostrogradski theorem
Great lecture from a great person..
great professor
Great intuitive explanation for the probability of finding the particle between a & b!
Amazing how he takes such a strange concept and makes it so easy to understand!
I agree. It is a wonderful quantum mechanics course I never joined.
What a great lecture!
as an engineer, i love this video, because there re tables!
Current is probability per unit time , or current is probability per unit time and unit area ?
I am also waiting for someone to explain this.
One dimensional is per unit time, three dimensional is per unit time per unit area
@@shubhamanand9414 Because in 3D the psi also need to fullfill normalization. \int|psi|^2dxdydz=1. So [psi] is L^-3/2
The current in the lecture is actually current density, so it is probability per unit time per unit area. The area(2 dimensional) is actually the area perpendicular to the current flow, so it only works in 3D. In 2D, current density is probability per unit time per unit length because the current is flowing perpendicular to a length(1 dimensional). In 1D, it is probability per unit time because the current is flowing perpendicular to 0 dimensions.
@@akashshfulthanks a lot
Muito obrigado
Thanks ❤️🤍
This is helpful ❤️🤍
The polydynamics of the movement generates pseudo-autonomy as material property, of the autogenous phenomenon; existing.(...)
Simultaneous as my unidimensional variability...
unidimensional variability = live-beings
I have seen the video of 28 and 29. There are problems. In this two section try to prove dN/dt=0. The condition is psi(x,t) is 0 at infinity. and d psi(x,t)/dt is bounded. This condition is is not enough. psi(x,t) is 0 at infinity is not enough. Assume psi(x,t) is proportion to 1/r, here r is distance from origin to the field point. Then psi(x,t) is 0 at infinity, but the integral along the surface to psi(x,t) is not 0. Even this surface is a sphere with its radius infinity.
Hence, psi(x,t) close to 0 faster than 1/r, at r -> infinity.
Don't call me a "unidimensional variability", please! ;-)
...but not the last...
Insightful lecture
Here are the solutions to Problem Set #2.
I do not guarantee their correctness.
Please edit, comment and correct.
docs.google.com/document/d/1M1Z4EVFY25RjeSOqw-iTt3ln_eFD9eU-zErn52mzEek/edit?usp=sharing
Hey mate, can you share your solution?
I done some maths, but not sure if it is correct :c
first