Experiments explained:
- via the Schrödinger equation solution for the hydrogen atom it predicts:
- spectral line basic lines, plus Zeeman effect
- Schrödinger equation solution for the helium atom: perturbative solutions give good approximations to the energy levels
- double-slit experiment: I think we have a closed solution for the max and min probabilities on the measurement wall, and they match experiments
Experiments not explained: those that the Dirac equation explains like:
- fine structure
- spontaneous emission coefficients
To get some intuition on the equation on the consequences of the equation, have a look at:
The easiest to understand case of the equation which you must have in mind initially that of the Schrödinger equation for a free one dimensional particle.
Then, with that in mind, the general form of the Schrödinger equation is:where:
Equation 1.
Schrodinger equation
. - is the reduced Planck constant
- is the wave function
- is the time
- is a linear operator called the Hamiltonian. It takes as input a function , and returns another function. This plays a role analogous to the Hamiltonian in classical mechanics: determining it determines what the physical system looks like, and how the system evolves in time, because we can just plug it into the equation and solve it. It basically encodes the total energy and forces of the system.
The argument of could be anything, e.g.:Note however that there is always a single magical time variable. This is needed in particular because there is a time partial derivative in the equation, so there must be a corresponding time variable in the function. This makes the equation explicitly non-relativistic.
- we could have preferred polar coordinates instead of linear ones if the potential were symmetric around a point
- we could have more than one particle, e.g. solutions of the Schrodinger equation for two electrons, which would have e.g. and for different particles. No matter how many particles there are, we have just a single , we just add more arguments to it.
- we could have even more generalized coordinates. This is much in the spirit of Hamiltonian mechanics or generalized coordinates
The general Schrödinger equation can be broken up into a trivial time-dependent and a time-independent Schrödinger equation by separation of variables. So in practice, all we need to solve is the slightly simpler time-independent Schrödinger equation, and the full equation comes out as a result.
Super Nintendo Entertainment System by 
Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01A switch is a box with a bunch of Ethernet wires coming into it:Except that it doesn't have to be Ethernet, e.g. it would also be a Wi-Fi.
+--------------------+
| +-+ +-+ +-+ +-+ |
| |1| |2| |3| |4| |
| +-+ +-+ +-+ +-+ |
+--------------------+What the switch does is:After the destination is found, a confirmation is somehow sent back to the switch, which then learns which wire to send each MAC address to.
- an Ethernet request came in from wire 1
- decide which wire to send it out on, e.g. wire 2, 3, 4, 5, etc. You likely don't want to send it back through 1 where it came from.
A switch is a bit like a router but it is a bit dumber/operates at a lower level: it basically operates only on MAC addresses, not on IP addresses.
The Internet service provider boxes most people have at home combines a switch for the local network and a router for the ISP communication.
From Wikipedia:and:
Multicellularity has evolved independently at least 25 times in eukaryotes
Complex multicellular organisms evolved only in six eukaryotic groups: animals, symbiomycotan fungi, brown algae, red algae, green algae, and land plants.
It seems impossible to avoid the signaling server. With signaling server:
Explicit scalar form of the Maxwell's equations by Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01For numerical algorithms and to get a more low level understanding of the equations, we can expand all terms to the simpler and more explicit form:
Every closed subgroup of is a Lie group by Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01 There are unlisted articles, also show them or only show them.