One who has knowledge of the Schrödinger Equation, will understand that it literally describes the law of attraction, aswell our non-dual nature.
When plotted on a graph in time, it can be observed the equation follows a straigt line on a point in "time". The imaginary "point" that follows the imaginary "line" is what in non-dual teachings / Taoism / Buddhism is called our "true nature".
It is this very equation that proves law of attraction. As at the very vore of the equation, the input desciibes the output. Simpler said: That what you believe, will shape your reality in some form.
Github - https://github.com/quantum-visualizations/qmsolve
QMsolve seeks to provide an easy solid and easy-to-use solver, capable of solving the Schrödinger equation for one and two particles, and creating descriptive and stunning visualizations of its solutions both in 1D, 2D, and 3D.
Example of the simulation of the eigenstates of a particle confined in two wells
Installation
pip install qmsolve
How the simulator works
The way this simulator works is by discretizing the Hamiltonian with an arbitrary potential, specified as a function of the particle observables. This is achieved with the Hamiltonian constructor.
Then, the Hamiltonian.solve the method efficiently diagonalizes the Hamiltonian and outputs the energies and the eigenstates of the system. Finally, the eigenstates can be plotted with the use of the visualization class.
The visualization.superpositionsmethod features the possibility of interactively visualizing a superposition of the computed eigenstates and studying the time dependence of the resulting wavefunction.
For a quick start, take a look at the examples found in the examples subdirectory.
Writing my PhD in literary studies, trying to make sure my scientific info is accurate.
Obviously, I recognize that the compound structure of the sentence probably simplifies the formalism of quantum mechanics beyond the point of usefulness, but still, is it wrong? Does it miss the relationship between various concepts?
If you can think of a better way to express all of the above in one sentence I won't say no to reading it.
Thanks!
I have the wavefunction in terms of x (radius) and X_0 (some constant maximum radius), as well as the potential term for a spherically symmetric potential for an l=0 system. I have the general form of the expectation energy for such a system, and am trying to find an expression for the expectation energy of for a specific given wavefunction by substituting into the general form. However, the integration limits in the given general form are (0, ∞). My wavefunction and potential function are valid for |x|<=X_0, and 0 elsewhere. I am unsure whether I should change the integration limits to (0,X_0), or to (-X_0,X_0). I have attempted to find the expression using the latter, and it was very messy. Integrating between (0,X_0) makes more sense to me physically, as a negative radius value doesn’t seem right, and that the original expression gives the lower integration limits as 0. But I am unsure due to the wavefunction being defined as valid for the modulus of x being less than the maximum radius. If somebody could tell me which integration limits I should use, and why, it would be much appreciated. Thanks!
I'm a high schooler who's been trying to self-learn quantum mechanics and I still don't fully understand the Schrödinger Equation. I would love a clear and understandable explanation including the mathematics and physics behind this equation. Pot of Coins for the best explanation for this equation.
For those of you who don't know what this is, here's the wikipedia page: https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation
Edit: I would like a detailed explanation, not one that's only a few sentences. i obviously know the basics of the Schrödinger Equation, I just don't understand the reasons behind the mathematics and physics. Also, I'll award in 1 day.
Edit: Challenge is over. u/Kvothealar has provided the best explanation.
I'm a physics undergraduate highly interested in this topic, but I haven't studied QFT yet.
It's quite ordinary to find in quantum physics texts discussing time-dependent perturbation theory applied to electron transitions, in which the hamiltonian consists of a time-varying classical electromagnetic field, for example, a Rabi 2 level system with an on-resonance electric field. The electron then sinusoidally oscillates between two states and acts as a dipole. This result is usually used to discuss stimulated emissions.
My point is, shouldn't the electron undergo some kind of recoil due to acting as a dipole and consequently losing energy in the form of photons in this process?
I know that even for a classical field is hard to model the radiation reaction for a single electron because it undergoes a contradiction with causality (Abraham–Lorentz force), so as I understand, in classical electromagnetism radiation reaction only makes sense when using a continuous charge distribution.
My question is, is there a way to way to account for radiation reaction in the Hamiltonian of a single electron?
I can imagine that this could involve computing the electric field created by the electron cloud, and then adding the energy of this field to the Hamiltonian computed with the following formula:
https://preview.redd.it/u71aio78aaa71.png?width=212&format=png&auto=webp&s=c876a285c30bd493813f2d9823700f22413dcc7c
The electric and magnetic fields E and B would be computed using Maxwell equations, where the charge density and the current density would be:
https://preview.redd.it/bltwp774taa71.png?width=125&format=png&auto=webp&s=74d2f5f1470e5d9d767dfec1e84bf5975603fba9
https://preview.redd.it/7cg3jkatsaa71.png?width=311&format=png&auto=webp&s=cf110a3a9b627151faea2d42343150f99f25f0be
So my final question is, does this Maxwell-Schrödinger system does have any sense and could approximate radiation reaction and stimulated emissions? And what about spontaneous emissions?
Someone told me that the Schrödinger equation can be converted into finding eigenvalues of a matrix. I haven't found anything about that though.
How can I do that and how can I use the eigenvalues to find the wave-function?
QFT courses build up complex practical notation, so that they can focus on illustrating the elegance and symmetry of QFTs, and extract useful results from them.
I’m looking for the opposite, stupid uninterpretable brute force. I’ll explain why at the end.
I want to expand out the Schrödinger equation for some QFT, say QED or the SM:
dψ/dt= (1/ iℏ) H ψ
Can I write ψ as an (infinite) vector of variables? Can I write H as an (infinite) matrix of constants? Can I multiply these out to give an infinite list of coupled first-order differential equations?
Notice how ‘yes you can do that but it’s stupid’, and ‘no you cannot do that, those aren’t even vaguely the right mathematical objects’ are profoundly different answers.
I'm in year 12 (lower 6th) and doing an essay on the Schrödinger equation, and one of the topics is going to be it's applications but I'm finding typing that into Google is far too broad so I thought I'd come here to narrow it down.
So far I've done particle in a box with the time independant equation, and I'll probably describe how the electron wave equation exists as a standing wave around the nucleus with integer wavelengths, but I haven't found much linking it to orbitals in the way that I'd hoped. Do I need to look into the 3 dimensional version, or integrating over a sphere? Seems like everywhere I look involves slightly different equations and ways it's used.
Thanks for the help.
I haven't researched too much into quantum mechanics, nor do I have any academical education, so I don't really understand a lot of the concepts in quantum mechanics, however, I have looked up a lot of things about quantum mechanics, and have a basic understanding of a lot of the equations in it. So my question is: why does ψ act as a variable in multiple equations? I understand that it represents the wave function, but how can the whole function be summarized into one value?
