Two identical bosons of mass m are placed in a one-dimensional potential 1 v(x)=mo'x². The bosons interact via a weak potential, V(* 2 V12 = V, expl- m2(x; -x,}° /4h %3D where and X2 denote coordinates of the particles. Given that the ground state 1 mox? wavefunction of the harmonic oscillator is y (x)=| 2h e The ground state energy of the two-boson system, to the first order in V,, is

What is the ground-state energy of (a) an electron and (b) a proton if each is trapped in a one-dimensional infinite potential well that is 273 pm wide? (a) Number 8.083824566 Units eV (b) Number 4.401408127 Units eV

You are given a free particle (no potential) Hamiltonian Ĥ dependent wave-functions = -it 2h7² m sin(2x) e = V₁(x, t) V₂(x, t) 2 sin(x)e -ithm + sin(2x)e¯ What would be results of kinetic energy measurements for these two wave-functions? Give only possible outcomes, for example, it is possible to get the following values 5, 6, and 7. No need to provide corresponding probabilities. ħ² d² 2m dx2 and two time- -it 2hr 2 m

An electron is in an infinite potential well of width 364 pm, and is in the normalised superposition state Ψ=cos(θ) ψ5-sin(θ) i ψ8. If the value of θ is -1.03 radians, what is the expectation value of energy, in eV, of the electron?