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Francesco Fucito
Complex Systems
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Article
Open AccessGauge theories on compact toric manifolds
We compute the \(\mathcal{N}=2\) N = 2 ...
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Book
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Chapter
Kinetic Physics
Determine the number of particle-wall collisions per unit area for an ideal quantum gas composed of N independent particles inside a cubic container of volume V. Treat the general case with a single particle ener...
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Chapter
Fermi-Dirac Gases
An atomic nucleus of Helium consists of a gas of 0.18 nucleons in a volume of 1 fm3 (1fm = 10−13cm). In this system, we can find two kinds of nucleons (protons And neutrons) with spin S=1/2 and their masses, m ...
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Chapter
Central Force Field
Let us consider a particle subject to the following three dimensional harmonic potential $$U\left( r \right) = \frac{{M{\omega ^2}{r^2...
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Chapter
Grand Canonical Ensemble
A gas is in contact with a surface. On the surface we find N 0 localized and distinguishable sites adsorbing N (N≤N 0) molecules of the gas (each site can adsorb zero or one molecu...
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Chapter
Bose-Einstein Gases
Consider a three dimensional gas of bosons with spin 0 and single particle energy given by $$\varepsilon = \frac{{{p^2}}}{{2m}}$$ ...
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Chapter
Angular Momentum and Spin
Determine the uncertainty relations between the orbital angular momentum $$\hat L = \left( {{{\hat L}_x},{{\hat L}_y},{{\hat L}_z}} \r...
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Chapter
Perturbation Theory and WKB Method
A plane rigid rotator has the following Hamiltonian $${\hat H_0} = \frac{{\hat L_z^2}}{{2I}}$$ where I is the momentu...
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Chapter
Canonical Ensemble
A classical gas in a volume V is composed of N independent and indistinguishable particles. The single particle Hamiltonian is $$H = \...
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Chapter
Formalism of Quantum Mechanics and One Dimensional Problems
Let Â=† be an observable operator with a complete set of eigenstates |ϕ n 〉 with eigenvalues α n (n=0, 1, 2,...). A generic state is given by
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Chapter
Thermodynamics and Microcanonical Ensemble
We know that the free energy F(T,V,N) of a thermodynamic system is extensive. Show that $$N{\left( {\frac{{\partial F}}{{\partial N}}}...
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Chapter
Fluctuations and Complements
Characterize the fluctuations of the energy in the grand canonical ensemble and prove that $$\left\langle {{{\left( {\Delta E} \right)...
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Chapter
Summary of Quantum and Statistical Mechanics
In Quantum Mechanics, the state of a particle in one dimension and in presence of a potential U(x,t), is entirely described by a complex wave function ψ(x,t) obeying the time dependent Schrödinger equation ...
