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Irrational Numbers and Quantum

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relationship between irrational numbers and quantum mechanics
why do these numbers apper in the equations of quantum mechanics: Visual of number line with marked rational and irrational numbers
In quantum physics, where things get fuzzy, there's this idea called the uncertainty principle. It says we can't nail down both a particle's speed and position at the same time. Kinda like how we can't pin down an irrational number on a number line because its decimal part goes on forever without repeating."
visuals of e and π appearing frequently in equations
: "In the math of quantum physics, we see numbers like e and π popping up a lot. They've got endless, non-repeating decimals, just like the weirdness of quantum stu on to visualization of the mass ratio calculation
r: "Now, think about the mass of a proton compared to an electron. It's a big deal in physics, coming in at around 1836.12. What's wild is, this number is super close to something totally different."
"If you multiply 6 by π raised to the fifth power, you get a number that's surprisingly close to the mass ratio we see in the real world."
Visual of proton and electron with text "The mysteries of quantum mechanics: Where math meets reality.
"In the mind-bending world of quantum physics, the dance between numbers and nature is both puzzling and beautiful. From the depths of weird numbers to the precise constants of our universe, it's a story that's as fascinating as it is mysterious."
Crystal Structure: Solids: Amorphous and Crystalline Materials. Lattice Translation
Vectors. Lattice with a Basis. Unit Cell. Miller Indices. Reciprocal Lattice. Types of
Lattices. Brillouin Zones. Diffraction of X-rays by Crystals. Bragg’s Law. Atomic
and Geometrical Factor. (14
Lectures)
Elementary Lattice Dynamics: Lattice Vibrations and Phonons: Linear Monoatomic
and Diatomic Chains. Acoustical and Optical Phonons.Qualitative Description of the
Phonon Spectrum in Solids.Dulong and Petit’s Law, Einstein and Debye theories of
specific heat of solids (qualitative only). T3 law (10
Lectures)
Magnetic Properties of Matter: Dia-, Para-, Ferri- and Ferromagnetic Materials.
Classical Langevin Theory of dia– and Paramagnetic Domains. Quantum Mechanical
Treatment of Paramagnetism. Curie’s law, Weiss’s Theory of Ferromagnetism and
Ferromagnetic Domains. Discussion of B-H Curve. Hysteresis and Energy Loss.
(12
Lectures)
Dielectric Properties of Materials: Polarization. Local Electric Field at an Atom.
Depolarization Field. Electric Susceptibility. Polarizability. Clausius Mosotti
Equation. Classical Theory of Electric Polarizability. Normal and Anomalous
Dispersion. Cauchy and Sellmeir relations. Langevin-Debye equation. Complex
Dielectric Constant. Optical ,Phenomena. Application: Plasma Oscillations, Plasma
Frequency, Plasmons.
(11 Lectures)
Elementary band theory: Kronig Penny model. Band Gaps. Conductors,
Semiconductors and insulators. P and N type Semiconductors. Conductivity of
Semiconductors, mobility, Hall Effect, Hall coefficient
Planck’s quantum, Planck’s constant and light as a collection of photons; Photo-
electric effect and Compton scattering. De Broglie wavelength and matter waves;
Davisson-Germer experiment.
(8 Lectures)
Problems with Rutherford model- instability of atoms and observation of discrete
atomic spectra; Bohr's quantization rule and atomic stability; calculation of energy
levels for hydrogen like atoms and their spectra. (6
Lectures)
Position measurement- gamma ray microscope thought experiment; Wave-particle
duality, Heisenberg uncertainty principle- impossibility of a particle following a
trajectory; Estimating minimum energy of a confined particle using uncertainty
principle; Energy-time uncertainty principle.
Two slit interference experiment with photons, atoms and particles; linear
superposition principle as a consequence; Matter waves and wave amplitude;
Schrodinger equation for non-relativistic particles; Momentum and Energy operators;
stationary states; physical interpretation of wavefunction, probabilities and
normalization; Probability and probability current densities in one dimension.
(11 Lectures)
One dimensional infinitely rigid box- energy eigenvalues and eigenfunctions,
normalization; Quantum dot as an example; Quantum mechanical scattering and
tunnelling in one dimension - across a step potential and across a rectangular potential
barrier. (12
Lectures)
Size and structure of atomic nucleus and its relation with atomic weight; Impossibility
of an electron being in the nucleus as a consequence of the uncertainty principle.
Nature of nuclear force, NZ graph, semi-empirical mass formula & binding energy.
(6 Lectures)
Radioactivity: stability of nucleus; Law of radioactive decay; Mean life and half-life;
decay; decay - energy released, spectrum and Pauli's prediction of neutrino; -ray
emission.
.
why do these numbers apper in the equations of quantum mechanics: Visual of number line with marked rational and irrational numbers
In quantum physics, where things get fuzzy, there's this idea called the uncertainty principle. It says we can't nail down both a particle's speed and position at the same time. Kinda like how we can't pin down an irrational number on a number line because its decimal part goes on forever without repeating."
visuals of e and π appearing frequently in equations
: "In the math of quantum physics, we see numbers like e and π popping up a lot. They've got endless, non-repeating decimals, just like the weirdness of quantum stu on to visualization of the mass ratio calculation
r: "Now, think about the mass of a proton compared to an electron. It's a big deal in physics, coming in at around 1836.12. What's wild is, this number is super close to something totally different."
"If you multiply 6 by π raised to the fifth power, you get a number that's surprisingly close to the mass ratio we see in the real world."
Visual of proton and electron with text "The mysteries of quantum mechanics: Where math meets reality.
"In the mind-bending world of quantum physics, the dance between numbers and nature is both puzzling and beautiful. From the depths of weird numbers to the precise constants of our universe, it's a story that's as fascinating as it is mysterious."
Crystal Structure: Solids: Amorphous and Crystalline Materials. Lattice Translation
Vectors. Lattice with a Basis. Unit Cell. Miller Indices. Reciprocal Lattice. Types of
Lattices. Brillouin Zones. Diffraction of X-rays by Crystals. Bragg’s Law. Atomic
and Geometrical Factor. (14
Lectures)
Elementary Lattice Dynamics: Lattice Vibrations and Phonons: Linear Monoatomic
and Diatomic Chains. Acoustical and Optical Phonons.Qualitative Description of the
Phonon Spectrum in Solids.Dulong and Petit’s Law, Einstein and Debye theories of
specific heat of solids (qualitative only). T3 law (10
Lectures)
Magnetic Properties of Matter: Dia-, Para-, Ferri- and Ferromagnetic Materials.
Classical Langevin Theory of dia– and Paramagnetic Domains. Quantum Mechanical
Treatment of Paramagnetism. Curie’s law, Weiss’s Theory of Ferromagnetism and
Ferromagnetic Domains. Discussion of B-H Curve. Hysteresis and Energy Loss.
(12
Lectures)
Dielectric Properties of Materials: Polarization. Local Electric Field at an Atom.
Depolarization Field. Electric Susceptibility. Polarizability. Clausius Mosotti
Equation. Classical Theory of Electric Polarizability. Normal and Anomalous
Dispersion. Cauchy and Sellmeir relations. Langevin-Debye equation. Complex
Dielectric Constant. Optical ,Phenomena. Application: Plasma Oscillations, Plasma
Frequency, Plasmons.
(11 Lectures)
Elementary band theory: Kronig Penny model. Band Gaps. Conductors,
Semiconductors and insulators. P and N type Semiconductors. Conductivity of
Semiconductors, mobility, Hall Effect, Hall coefficient
Planck’s quantum, Planck’s constant and light as a collection of photons; Photo-
electric effect and Compton scattering. De Broglie wavelength and matter waves;
Davisson-Germer experiment.
(8 Lectures)
Problems with Rutherford model- instability of atoms and observation of discrete
atomic spectra; Bohr's quantization rule and atomic stability; calculation of energy
levels for hydrogen like atoms and their spectra. (6
Lectures)
Position measurement- gamma ray microscope thought experiment; Wave-particle
duality, Heisenberg uncertainty principle- impossibility of a particle following a
trajectory; Estimating minimum energy of a confined particle using uncertainty
principle; Energy-time uncertainty principle.
Two slit interference experiment with photons, atoms and particles; linear
superposition principle as a consequence; Matter waves and wave amplitude;
Schrodinger equation for non-relativistic particles; Momentum and Energy operators;
stationary states; physical interpretation of wavefunction, probabilities and
normalization; Probability and probability current densities in one dimension.
(11 Lectures)
One dimensional infinitely rigid box- energy eigenvalues and eigenfunctions,
normalization; Quantum dot as an example; Quantum mechanical scattering and
tunnelling in one dimension - across a step potential and across a rectangular potential
barrier. (12
Lectures)
Size and structure of atomic nucleus and its relation with atomic weight; Impossibility
of an electron being in the nucleus as a consequence of the uncertainty principle.
Nature of nuclear force, NZ graph, semi-empirical mass formula & binding energy.
(6 Lectures)
Radioactivity: stability of nucleus; Law of radioactive decay; Mean life and half-life;
decay; decay - energy released, spectrum and Pauli's prediction of neutrino; -ray
emission.
.
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