What is 1d harmonic oscillator: Definition and 15 Discussions
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hi guys
i am trying to solve the Asymptotic differential equation of the Quantum Harmonic oscillator using power series method and i am kinda stuck :
$$y'' = (x^{2}-ε)y$$
the asymptotic equation becomes :
$$y'' ≈ x^{2}y$$
using the power series method ##y(x) = \sum_{0}^{∞} a_{n}x^{n}## , this...
I have got a simple qstion.
We have a particle in 1d oscillator with E0( fundamental level).We know that phi~ e^-x^2 for any x, so We can measure a position and get a value x=a, such that V(a)>E0 . In this case T<0 so the velocity of the particle is imaginary, how is this even possible?, (a real...
Homework Statement
Show that for the one-dimensional linear harmonic oscillator the Hamiltonian is:
[; H = \frac{1}{2}[P^2+\omega ^2 X^2]-\frac{1}{2}\omega \hbar ;]
[; =\frac{1}{2}[P+i\omega X][P-i\omega X]+\frac{1}{2} \omega \hbar ;]
where P, X are the momentum and position operators...
The ground state wave-function of a 1-D harmonic oscillator is
$$
\psi(x) = \sqrt\frac{a}{\sqrt\pi} * exp(-\frac{a^2*x^2}{2}\frac{i\omega t}{2}).
$$
a) find Average potential energy ?
$$
\overline{V} = \frac{1}{2} \mu\omega^2\overline{x^2}
$$
b) find Average kinetic energy ?
$$
\overline{T} =...
Hey, I'm stuck halfway through the solution it seems. I could use some tips on how to continue.
1. Homework Statement
I have to determine a linear combination of the states |0\rangle, |1\rangle, of a one dimensional harmonic oscillator, so that the expectation value \langle x \rangle is a...
Homework Statement
Hello,
I'm just curious as to whether I'm going about solving the following problem correctly...
Problem Statement:
A particle mass m and charge q is in the ground state of a one -dimensional harmonic oscillator, the oscillator frequency is ω_o.
An electric field ε_o is...
Homework Statement
The generalization of the bohr rule to periodic motion more general than circular orbit states that:
∫p.dr = nh = 2∏nh(bar).
the integral is a closed line integral and the "p" and "r" are vectors
Using the generalized rule (the integral above), show that the spectrum for...
Hi. I want to write the entropy of a 1d harmonic oscillator as a function of energy, but for each energy there is only one possible configuration. So is the entropy zero? I mean, the energy is E=hw(n+1/2), so there is only one microstate for each energy.
Hi, I'm currently working through some exam papers from previous years before an upcoming module in Quantum Mechanics.
Homework Statement
See the attached image
Homework Equations
The Attempt at a Solution
I'm a little stumped with this one, I'm assuming that I'm looking...
I Have a brief idea about the equation and i have searched the web for its application to one dimensional harmonic oscillator but no use. Any Help Would Be Welcomed Especially about the latter:smile:
Homework Statement
Find the eigenvalues and eigenfunctions of H\hat{} for a 1D harmonic oscillator system with V(x) = infinity for x<0, V(x) = 1/2kx^2 for x > or equal to 0.
Homework Equations
The Attempt at a Solution
I think the hamiltonian is equal to the potential + kinetic...
Homework Statement
"Two non-interacting particles are placed in a one-dimensional harmonic oscillator potential. What are the degeneracies of the two lowest energy states of the system if the particles are
a)identical spinless bosons
b)identical spin-1/2 fermions?
Homework Equations...
Hi. I have recently designed a simulator about Qunatum Mechanics one dimensional harmonic oscillator. Please try it. I will be glad to read your opinions.
http://erham.persiangig.ir/Programs/1386/QM1DHOS10.png
Size: 223 KB
http://erham.persiangig.ir/Programs/1386/QM1DHOS10.zip"
Homework Statement
particle in ground state of 1D harmonic oscillator - spring constant is doubled - what is the probability of finding the particle in the ground state of the new potential
Homework Equations
v=1/2kx^2 oscillator potential
wavefunction ground state n=0 =...