Two identical non-interacting particles of rest energy 0.1973 MeV are trapped in the sameinfinitely deep one-dimensional square well of width 0.625 µm . If the total energy of thetwo-particle state is 0.31568 ueV, write down the two-particle wave function in each of thefollowing cases:1. the particles are spinless;2. the particles are electrons and the spin of the state is s = 0;%3D3. the particles are electrons and the spin of the state is s = 1;%3D4. When the Coulomb repulsion between the electrons is taken into account in2 and3 , which spin state will have the lower energy?

Answered: Image /qna-images/answer/b4bb2e32-e85f-4765-b2e5-65060287db34.jpg

Answered: Two identical non-interacting particles…

Similar questions

An electron is confined to a box of width 0.25 nm. Calculate the wavelengths of the emitted photons when the electron makes transitions between the fourth and the second excited states.
Consider the Bloch sphere for a single qubit. What is the state represented by the Bloch vector (-1,0,0)? (12+) - i|z_)) a. b. |z_) c. (z+) d. • e. (12+)+ 12-)) (12+) - 12-))
3. Particle in a 2D Box. A quantum mechanical particle is confined in side a square 2D box, with side length L. Inside the box V=0 and outside the box V=infinity. Let the wave function to be (x,y). (a) write down the Schrodinger equation of (x,y). (b) Use the separation of variable method solve (x,y) (let the quantum numbers to be nx and ny.) (c) What is the energy for the state (nx, ny)? (d) What is the probability density p(x,y) for the state nx=3 and ny=3? Sketch this p(x,y) in a square.
The average lifetime of a Z boson is about 3.0 x 10 J Need Help? Read It -25 s. Estimate the minimum uncertainty in the energy of a Z boson.
Q7B2
An electron in a hydrogen atom failing from an excited state (n=7) to a relaxed state has the same wavelength as an electron moving at a speed of 7281 m/s. Determine the relaxed orbit that this electron relaxed to.
B7
4. Normalize the following wavefunctions 4 55 (a) v(x) = sin (#2); =sin(); for a particle in a 1D box of length L. (b) (2) = xe-z|2 (c) (x) = e(x²/a²)+(ikz) 5. In a region of space, a particle with mass m and with zero energy has a time- independent wave-function (x) = Ae-2/12, where A and L are constants. Use your knowledge of the Schrödinger equation to determine the potential energy V(x) of the particle. Plot the potential function? What is the minimum potential energy for the particle, if it is an electron and L = 1 fm? Is this potential repulsive or attractive?