A particle of mass m moves in the potential V(x) = -g*delta(x) x>-a infinity x<-a (delta (x) = dirac delta function) a. Without worrying about continuity or boundary conditions, write down the general solution of the Schrodinger equation for a bound state (energy E<0) in regions( -a less than x les ...continues
Time dependent Schrodinger equation (TDSE) in operator from
Time dependent Schrodinger equation (TDSE) in operator from. (Pls refer to the attached jpg)
Estimate the ground state energy of a particle of mass m moving in the potential V(x) = lambda *(x)^4 by two different methods. a. Using the Heisenberg Uncertainty Principle; b. Using the trial function psi(x)=N*e^{[- abs(x)]/(2a)} where a is determined by minimizing (E) *Note abs = absolute value
Find Hermitian Conjugate of (d/dx)(x^2)(d^2/dx^2) + (1 + 3i)xd/dx
Note that all the derivatives in the problem are partials with respect to x, and the i is an imaginary number Find the Hermitian Conjugate (operator O-dagger) of the operator O (operator) = (d/dx)*(x^2)*(d^2/dx^2) + (1 + 3i)*x*d/dx
1D motion of a quantum particle in an external potential with it's total energy
1D motion of a quantum particle in an external potential with it's total energy given by: (Please refer to the attached jpg)
Relative states and Hidden Variables in Quantum Mechanics
I ONLY NEED HELP WITH NUMBER ONE. It looks really long but the beginning is just a set up to the question. Skip to 'Your job' to see the question. I don't understand this stuff at all so if you could guide me through this step by step it would be appreciated. Explanations are important.
A particle moving in a delta potential with positive energy
A particle of mass m, with energy E>0, is moving in the potential
V(x)=g[delta(x+a) + delta(x-a)]
Assuming that the particle is incident from the left, what is the solution of the Schrodinger equation in all three regions (x
Kinetic and potential energy of harmonic oscillator, virial theorem
(See attached file for full problem description) --- 1. Consider a particle moving in a harmonic oscillator potential V(x) = ½ kx2. A solution of the time-dependent Schrodinger equation is cn n(x)*e –i * E(n) * t / h-bar where the n are harmonic oscillator energy eigenstates. a. Calculate the energy expect ...continues
(See attached file for full problem description)
---
2. A particle of mass m is constrained to move between two concentric, impermeable spheres of radii r = a and r = b. The potential V( r ) = 0 between the spheres (a
Angular States in Quantum Mechanics
(See attached file for full problem description) --- 3. Let denote the eigenstates of L2 and Lx; i.e. L2 = l(l+1)h-bar2 and Lx = m*h-bar* a. Explain briefly why you can always express any given as a superposition of spherical harmonics Yl’m’ with l’=l. b. In particular, for each m = +1,0,-1, find the constants a, ...continues
