In the paper
C. S. Lent and P. D. Tougaw, "A device architecture for computing with quantum dots," in Proceedings of the IEEE, vol. 85, no. 4, pp. 541-557, April 1997, doi: 10.1109/5.573
about quantum dots, it is stated that the basis vectors in the space of quantum states for a single cell...
I have the following differential equation, which is the general Sturm-Liouville problem,
$$
\dfrac{d}{dx} \left[ p(x) \dfrac{d\varphi}{dx} \right] + \left[ \lambda w(x) - q(x) \right] \varphi(x) = 0\ ,
$$
and I want to perform the change of variable
$$
x \rightarrow y = \int_a^x \sqrt{\lambda...
The hamiltonian ´for a free falling body is $$H = \dfrac{p^2}{2m} + mgy$$ and since we are using cartesian coordinates that do not depend on time and the potential only depends on the position, we know that ##H=E##. For this hamiltonian, using the Hamilton's equations and initial conditions...
A mass ##m## is restricted to move in the parabola ##y=ax^2##, with ##a>0##. Another mass ##M## is hanging from this first mass using a spring with constant ##k## and natural lenghth ##l_0##. The spring is restricted to be in vertical position always. The coordinates for the system are ##x##...
In order to compute de lagrangian in spherical coordinates, one usually writes the following expression for the kinetic energy: $$T = \dfrac{1}{2} m ( \dot{r}^2 + r^2 \dot{\theta}^2 + r^2 \sin^2 \theta \dot{\phi}^2 )\ ,$$ where ##\theta## is the colatitud or polar angle and ##\phi## is the...
You are plotting just one point at the end, with coordinates (maxiter + 1, x(maxiter + 1)).
If you want to plot ##g(x)##, you should do something like this (for example before calculating the fixed-point):
x= -10:0.01:10;
g = x^5-3*x^3-2*x^2+2;
plot(x, g);
After this, you should calculate the...
I would better say that, if ##f## and ##g## are valid wavefunctions, then both belong to the complex space ##L_2(\mathbb{R})##, which is a Hilbert space if we consider the scalar product defined as
$$
\langle f | g \rangle = \int_{-\infty}^{\infty} f^*(x)g(x)\ dx\ .
$$
By definition, the...
I think those are interesting questions and I will try to answer it briefly but with enough explanations. Also, consider that I'm not an expert in this area, so I may be wrong in some details, although I have been studying quantum computing seriously for some time for my master thesis, so I...