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Physics Travel Guide – Physics concepts explained in three levels of difficulty

physicstravelguide.com

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Re: Physics Travel Guide – Physics concepts explained in three levels of difficulty

#31

Post by scythe »

monktastic1 wrote: post #28

I found this section confusing (emphasis mine): https://physicstravelguide.com/equations/schroedinger_equati... "This means that for all systems where the Hamiltonian does not explicitly depend on the time, we known (sic) immediately how the time-dependence of the total wave function Ψ(x,t) looks like (sic), namely: Ψ(x,t) = phi(t)ψ(x) = Ae^(−Et/ℏ)ψ(x). The only thing we then have to do is to solve the stationary Sch…

>Ψ(x,t) = phi(t)ψ(x) = Ae^(−Et/ℏ)ψ(x)

This equation is missing a sum symbol, also it should be e^(-iEt/ℏ), where in the correct case the amplitude does not change. What you get is a sum of products of each occupied stationary state and a time-dependent phase. So the general solution looks like this:

https://en.wikipedia.org/w/index.php?title=User:Scythe33/san...

Re: Physics Travel Guide – Physics concepts explained in three levels of difficulty

#32

Post by monktastic1 »

contravariant wrote: post #30
monktastic1 wrote: post #28

I found this section confusing (emphasis mine): https://physicstravelguide.com/equations/schroedinger_equati... "This means that for all systems where the Hamiltonian does not explicitly depend on the time, we known (sic) immediately how the time-dependence of the total wave function Ψ(x,t) looks like (sic), namely: Ψ(x,t) = phi(t)ψ(x) = Ae^(−Et/ℏ)ψ(x). The only thing we then have to do is to solve the stationary Sch…

You have misread slightly I fear. Note that he says: >the stationary Schrödinger equation Hψ(x) = Eψ(x)." which is not the original Schrödinger equation, but a Schrödinger equation which is stationary and which forms part of the solution of the original Schrödinger equation.

Thanks. That's the context I was referring to. Reading the whole thing again twice more, I can still confidently say it would have confused me more than helped me when I was first learning.

Re: Physics Travel Guide – Physics concepts explained in three levels of difficulty

#33

Post by monktastic1 »

scythe wrote: post #31
monktastic1 wrote: post #28

I found this section confusing (emphasis mine): https://physicstravelguide.com/equations/schroedinger_equati... "This means that for all systems where the Hamiltonian does not explicitly depend on the time, we known (sic) immediately how the time-dependence of the total wave function Ψ(x,t) looks like (sic), namely: Ψ(x,t) = phi(t)ψ(x) = Ae^(−Et/ℏ)ψ(x). The only thing we then have to do is to solve the stationary Sch…

>Ψ(x,t) = phi(t)ψ(x) = Ae^(−Et/ℏ)ψ(x) This equation is missing a sum symbol, also it should be e^(-iEt/ℏ), where in the correct case the amplitude does not change. What you get is a sum of products of each occupied stationary state and a time-dependent phase. So the general solution looks like this: https://en.wikipedia.org/w/index.php?title=User:Scythe33/san...

Indeed. But as another commenter points out, what I think they wanted was to solve only for eigenstates here. Apparently I'm not the only one this confused.

Re: Physics Travel Guide – Physics concepts explained in three levels of difficulty

#34

Post by mhh__ »

magv wrote: post #23

From just glancing at a few articles, this site is a treasure trove of references to highly readable explanations on a variety of fairly advanced topics. In fact, just the links to Wilczek's grand unification overview [1], and Klauber's Student Friendly QFT book [2,3] made this site worth visiting for me. Resources that explain physics in (relatively) simple language without requiring books worth of prior knowledge s…

I haven't read it in full but Klauber's book is supposedly loaded with errors and also (in my view) needs re-typesetting (it's written in word)

Re: Physics Travel Guide – Physics concepts explained in three levels of difficulty

#36

Post by qubots »

spodek wrote: post #13

Almost nothing about experiments. Physics is an experimental science, based on observation of nature. Its treatments of experiments is as if they were mere side notes to the real thing. The Tools section might include something like a ruler, clock, or basic physical tools used to observe nature with.

> Physics is an experimental science, based on observation of nature.

I strongly disagree with this. In my first undergrad QM course I barely learnt anything about experiments. Experiments are quite important, but they are just side notes to the real thing.

Experiments are a way to check whether certain theories make sense, but not all theories. Many concepts have been proven mathematically, but have not yet been tested through experiments. Does that mean that theories are not part of physics? How do we know how elementary particles behave on a scale so small that we can’t observe their behaviour?

When we’re not able to acquire data, what's left for us is to construct new theories purely based on mathematics. Physics does not end where we can’t do observations, it actually starts exactly there.

Re: Physics Travel Guide – Physics concepts explained in three levels of difficulty

#38

Post by 8bitsrule »

johndoe42377 wrote: post #7

Some of those articles are just a modern Tantra - no one is seriously trying to refute these models because lots of people have a comfortable, high social status living out of it, just like modern theologians or tibetologists - they know the mantras and it's current interpretations, and the question of "How real it is" is frowned upon. Generalisations aside (however valid and useful) most of this theoretical physics…

An 'esoteric tradition' cannot be overturned by direct observation available to anyone.

To an extent, there's certainly an 'esoteric priesthood' in many sciences which can be quite dogmatic about certain models. It's certainly true that valuable observations will sometimes be ignored for a time - but eventually, theory increasingly fits observation.

It's certainly not a 'nothing but' in the same sense as tantra. The predictive power of theories is essential to their fame. Einstein's early 1900s models - which seriously refuted earlier models - anticipated many later observations.

Esoteric traditions like tantra have been overturned by the experiences of one individual and the insights they transmit to others. All part of the same play.

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