Solve the for the energy eigenvalues and eigenfunctions for a particle in a 1D box such that the box has a length LL and is centered about the origin of a coordinate system. Find values of mL2mL2 such that the particle becomes relativistic, it hardly moves, or moves with the speed of an airbus in its ground state.

Q: Consider an electron in the hydrogen atom. The electron is initially in the groundstate. a) If…

A:

Q: Which of the following functions are eigenfunctions of the momentum operator? a)eikx, b)eax2, c)x,…

A: Given that, some functions are eikx eax2 x x2 ax+b sin(x+3a) We have to determine among the given…

Q: Consider the oscillator with the following wavefunction: wavefunction = Cxe^(-ax^2) Starting with…

A: Given thatAs we use here Schrodinger equation that is expressed in equation 1Now substitute the…

Q: (a) Consider a wavefunction of the form: =1+x-1<x<0 v(x) =1-x 0<x<1 i) Normalise the wavefunction…

A: To normalize the wavefunction, we need to determine the normalization constant A such that the…

Q: Calculate the expectation values of x and x2 for a particle in the state with n = 1 in a…

A: The expectation value of x2 for a particle is given by following expression. The value of ψ for one…

Q: 1. Hermitian operators. Specify (show) which of the following operators are Hermitian: (a) id/dx and…

A: Hermitian operator- An operation is said to be hermitian if it follows: A=Aτ It is also known as…

Q: Which of the following wavefunctions are eigenfunctions of the operator

A:

Q: If two functions f (x ) and g (x ) are both eigenfunctions of some hermitian operator, what does it…

A: Eigenfunctions are the functions which contains information about the state of the system and which…

Q: Let operator Ĥ. Let be one of the normalized eigenfunctions of a Hamiltonian be an approximation of…

A: The equation given is:Where: is one of the normalized eigenfunctions of the Hamiltonian operator .…

Q: Do the total energy and the momentum operators commute? If yes, determine the eigenvalue. If not,…

A: To predict whether the total energy and the momentum operators commute or not.

Q: 3) Consider an arbitrary operator A. A operates on any function to its right. Here are the results…

A: Let an equation is,     Âx = ax  Where the operator(Â), operating on a function(x), produces a…

Q: Find the eigenvalues and eigenstates of the spin operator S; of an electron in the direction of a…

A: Assuming a unit vector n⏞ = j^ cosα + k^ sin α where  α = angle made by unit vector with y-axis The…

Q: Do the kinetic energy operator and momentum operator commute once they are applied on f(x) =AX?

A:

Q: Using the original definition of the momentum operator and the classical form of kinetic energy,…

A:

Q: 2. Show that the set of one-dimensional particle in the box functions where n = 1,2,3... are…

A: The proof is given as follows:

Q: 10. Frist few harmonic oscillator wave functions. (i) Plot/draw (sketch/draft) the first four (4)…

A: The concept used in this question is taken from Simple Harmonic Oscillator of Quantum Chemistry.…

Techniques and applications of quantum theory

Quantum theory, often known as quantum physics, is the foundation of modern physics and encompasses the nature and behavior of matter and energy at the atomic and molecular levels. As the exact nature and behavior of atomic and subatomic particles are impossible to determine, the laws of classical physics do not apply to this discipline. As a result, quantum field theory is primarily based on assumptions and probabilities.