This equation is of the form,
And its soluton is given by,
In this case,
So, we have our solution,
so we have,
So, from this we have,
So, our wave equation is given by,
Or putting the value of k,
b)
For spatial period, that is the wavelength, we find the distance between the two alternate points where this function vanishes
So,
Distance between alternate point = 2*pi,
So,
c)
Given that,
So, we get,
Free quantum particle. In Quantum Mechanics, is the time-independent Schrodinger's equation for a free particle in...
a) What is Schrodinger's equation for a particle of mass m that is constrained to move in a circle of radius R, so that psi depends only on phi? b) Solve this equation for psi and evaluate the normalization constant. (Hint: review the solution of Schrodinger's equation for the hydrogen atom) c) Find the possible energies of the particle. d)Find the possible angular momenta of the particle.
QUESTION 1: In quantum mechanics, the behaviour of a quantum particle (like an electron, for example) is described by the Schrödinger equation. The time-independent Schrödinger equation can be written in operator notation as H{y(x, y, z))-Ey(x, y, z) where H is known as the Hamiltonian operator and is defined as h2 2m Here, is a positive physical) constant known as Planck's constant and m is the mass of the particle (also Just a constant). V(x,y,Z) is a real-valued function. The...
-36 Imagine an alternate universe where the value of the Planck constant is 6.62607x 10J- In that universe, which of the following objects would require quantum mechanics to describe, that is, would show both particle and wave properties? Which objects would act like everyday objects, and be adequately described by classical mechanics? object quantum or classical? classical A human with a mass of 70. kg, 2.4 m high, moving at 4.5 m/s. quantum classical A ball with a mass of...
What would be the result of a kinetic energy measurement on a free quantum particle? (i.e. potential energy V(x) = 0) of mass m with a wave-function ψ(x) = e^(-x^2) A hint for this question: Consider only the kinetic energy operator. Is the given function an eigenfunction of this operator? If yes, what will be the result of the measurement? If not an eigenfunction, what would be the result of the measurement?
Introduction to Quantum Mechanics problem: 3. Find the normalized stationary states and allowed bound state energies of the Schrodinger equation for a particle of mass m and energy E < Vo in the semi-infinite potential well Vo 0.
The time-independent Schroedinger equation is given by: − Wave functions that satisfy this equation are called energy eigenstates. a) If U=0 for all positions, this represents a free particle. For a wave function with definite momentum ℏ,, compute E. b) Is the relationship derived from a) consistent with what we know from classical mechanics for a free particle? Explain how or how not. c) Consider the wave function ((^b[j + ^bâj), with A some number and c, d not equal...
Mechanics. 3. A particle of mass m moves in one dimension, and has position r(t) at time t. The particle has potential energy V(x) and its relativistic Lagrangian is given by where mo is the rest mass of the particle and c is the speed of light (a) Writing qr and denoting by p its associated canonical momenta, show that the Hamiltonian is given by (show it from first principles rather than using the energy mzc2 6 marks (b) Write...
Question #9 all parts thanks 9. The wavefunction, p(x,t), of a particle moving along the x-axis, whose potential energy V(x) is independent of time, is described by the one-dimensional non-relativistic Schrödinger equation (where m is its mass, h is the reduced Planck constant, i is the imaginary number): 2m (a) Verify that it is a parabolic equation (page E-1-2). [It has wave-like solutions, however.] (b) Use the substitution Px,t)-Xx)Tt) to separate the equation into two ODEs. (c) Solve for T,...
Question 21 Consider a free electron in one dimension (i.e. an electron free to move along say the x-direction on (a) The time-independent Schrödinger equation is Αψη (x)-Εηψη (x), where is the Hamiltonian (total energy) operator, and ψη (x) are the electron wave functions associated with energies En Assuming the electron's energy entirely comprises kinetic energy (as it is 'free' there is no potential energy term), write down the Schrödinger equation given that the momentum operator in one- dimension is...
Quantum Mechanics Please help me to solve this exercise step by step. I will appreciate it a lot. Write clear 2. An important problem of quantum mechanics is that of the particle subject to a linear res- titutive force (harmonic oscillator). The stationary Schrödinger equation for this problem, in one dimension, has the form h² #20 Ika-6 = EⓇ 2m 8x2 + 2k2O = Eº where k is the oscillator constant. Solutions of the following types are proposed: a) 6...