Physics and Mathematics as an ai tool

It seems to be unanble to calculate the following term:

F = 8,98810^9 * (1,22510^-9 / 0,0144) = 764,6 N

Itā€™d be nice if it could solve Quantum Mechanics related problems Accurately such as:

a) Using a Gaussian trial function e^(-Ī»x^2), with an adjustable parameter Ī», make a variational estimate of the ground state energy for a particle in a Gaussian potential well, represented by the Hamiltonian:

H = P^2 / (2m) - V0e^(-Ī±x^2)

(b) Consider the radial part of the Schrƶdinger equation for the hydrogen equation:

(-ħ^2 / (2m)) [1/r^2 d/dr (r^2 d/dr) - e^2/r]R(r) = ER(r)

Supposed we didnā€™t know the exact ground state for this system and we adopted the variational test wavefunction:

R_Ī± = Ce^(-Ī±r^2), Ī± > 0

(i) What is the integral expression for the energy with this test wave function? Explain the origin of each factor in the integral.

(ii) What is the numerical value of the ground state with this test wave function? Compare it with the actual ground state energy of the hydrogen atom.

Itā€™d be nice if the AI could solve orbital dynamics problems for planning launch windows, burn maneuvers, and planetary slingshots for solar system probesā€¦ :melting_face:

If AI could do substantial math research on its own ā€¦ then you know AGI has arrived.

Thatā€™s my definition at least.

Right now AI is trying to mimic the human senses through repetitive pattern matching. Things like Audio, Visual, and Text.

Math is hard because of the lack of self-play and the infinite action space (ref)

So pretty much brick wall until we can substantially surpass ā€œspicy autocompleteā€ :rofl:

1 Like

The body moves according to the equation S=40t-0.1tĀ². How long after the start of the movement will the body stop? Find the speed of the body at the end of the 5th second of the movement.

Hi and welcome to the Developer Forum!

It seems like you are looking for ChatGPT! This is not it, you can find it over at https://chat.openai.com