# Search results

1. ### I Can this particular method solve these quadratic equations?

Given are two equations: $$S_1 = ax^2+2hxy+by^2 + c=0$$ $$S_2 = a'x^2+2h'xy+b'y^2 + c'=0$$ This source states that there are several methods to solve for ##x## and ##y##. One of them is the following quote:"Treat equation ##S_1## as a quadratic equation in ##x## and solve it for ##x## in terms...
2. ### I Correlation between Symmetry number & Total wavefunction

Some rotational quantum states are not allowed for a rotating particle. At quantum level, these "forbidden" quantum states is based on the requirement of the total wavefunction being either symmetrical or anti-symmetrical, depending on whether the particle is a fermion or boson. The particle's...

9. ### I The Classical Limit of Maxwell-Boltzmann Distribution

I have been reading about the quantum effects that limit the Maxwell-Boltzmann Distribution under certain conditions which leads to the Bose-Einstein or Fermi-Dirac Distribution. I have difficulty grasping the reasons why these quantum-effects occur only at certain conditions and why exactly...
10. ### B Opening boxes consecutively to find 1 prize

I've seen a simple guessing show but I'm a bit surprised by its probability results and don't know what I'm doing wrong. A prize is hidden in 1 of 7 boxes and a person has to guess in which box it is. He opens a box one after the other and I questioned myself what the probability might be for...
11. ### I Calculating the number of energy states using momentum space

A question came up about deducing the number of possible energy states within a certain momentum ##p## using momentum space. To make my question easier to understand, I deliberately chose ##p## and not a particular increment ##dp## and I assume a 2 dimensional momentum space with coordinates...
12. ### Questions about deriving the Maxwell-Boltzmann Distribution

Hello, I was watching a video on the derivation of the Maxwell-Boltzmann distribution function which would eventually lead to: $$\frac{e^{-\beta \cdot \epsilon_i}}{\sum_{i=0}^n e^{-\beta \cdot \epsilon_i}}$$ To do this, initially, the number of possible permutations ##\Omega## of a total of...

29. ### I Calculating planet's radius using a star's luminosity

Hello, I’ve been watching a lecture about how in astronomy one would be able to calculate the radius of 2 stars by measuring the velocity of the orbit and then measure the time how long the luminosity of a star dims when one star is behind the other. After thinking this a bit through, I came...
30. ### I Circular area on a sphere

I had a question regarding calculating the area of a circular cap on a sphere. From what I’ve read, the area should be calculated according to; $$A = 2πr^2 \cdot (1 – cos (\frac{θ}{2} )$$ However, I have another way but I don’t understand why this isn’t correct. The circular area can be...