• Water Waves

    Most water waves are formed as a result of changes in the pressure and velocity of air close to the water surface. The largest waves are however formed by tides, currents, earthquakes etc. Increasing windspeed is associated with increasing wave height....

    https://astarmathsandphysics.com/university-physics-notes/fluid-mechanics/1583-water-waves.html

  • Water Waves on a Sloping Beach

    To the landperson waves are most encountered at the beach, or swimming near the beach. Far from the beach the waves are nearly uniform progressive waves with wavelength from a few metres to a few hundred metres and speeds ranging from 4m/s to 20m/s....

    https://astarmathsandphysics.com/university-physics-notes/fluid-mechanics/1584-water-waves-on-a-sloping-beach.html

  • Constants

    Avagadro's Constant Planck's Constant Mass of Electron Mass of Proton Mass of neutron Elementary Charge Bohr Magneton Bohr Radius Compton Wavelength of Electron Coulomb's Law Constant Electron Charge to Mass Ratio Rydberg Constant for Hydrogen Speed of...

    https://astarmathsandphysics.com/university-physics-notes/quantum-mechanics/1626-constants.html

  • Dispersion Relations

    A particle does not occupy a fixed, definite position in space. It is smeared out over a definite none zero volume in the form of a wavepacket. In general the wavepacket is made of of many differentfrequencies or wavelengths. They interfere...

    https://astarmathsandphysics.com/university-physics-notes/quantum-mechanics/1627-dispersion-relations.html

  • Features of Bound State Wavefunctions

    The particle moves fastest in regions of minimum potential energy. Since it moves fastest and has most energy there, it's wavelength is shorter. It spends least time in those regions and so the probability of finding the particle there is low, hence is...

    https://astarmathsandphysics.com/university-physics-notes/quantum-mechanics/1629-features-of-bound-state-wavefunctions.html

  • Features of Solutions of the Schrodinger Equation for the Hydrogen Atom

    The general solution of the Schrodinger equation corresponding to a principal quantum number is a polynomial in of degree with circles of zero electron density multiplied by a polynomial in ( or or both) of degree with radial lines of zero electron...

    https://astarmathsandphysics.com/university-physics-notes/quantum-mechanics/1630-features-of-solutions-of-the-schrodinger-equation-for-the-hydrogen-atom.html

  • Hermitian Operators

    Quantum Mechanical operators are hermitian. If a quantum mechanical operator is represented by a matrix then so that is equal to the complex conjugate transpose of For example, the spin Pauli operators may be represented by the matrices Every quantum...

    https://astarmathsandphysics.com/university-physics-notes/quantum-mechanics/1631-hermitian-operators.html

  • Linear Combinations of Eigenfunctions

    An eigenfunction which represents a possible state of a particle is any solution of the Schrodinger equation which may be written in the form where A linear combination of any number of eigenfunctions is also a possible wavefunction. Proof: Hence the...

    https://astarmathsandphysics.com/university-physics-notes/quantum-mechanics/1632-linear-combinations-of-eigenfunctions.html

  • Normalizing the Wavefunction

    The Born interpretation gives the probability of finding a particle with wavefunction - I have shown the wavefunction here to be a function of here, though I need not have done and do not use this below - in the volume of space between and is The...

    https://astarmathsandphysics.com/university-physics-notes/quantum-mechanics/1633-normalizing-the-wavefunction.html

  • Probability Current or Probability Flux

    The probability density of a particle with wavefunction – or statefunction – is The probability density function changes in space, but it may also change in time. If the probability density is a function of time, then the particle will be moving and...

    https://astarmathsandphysics.com/university-physics-notes/quantum-mechanics/1635-probability-current-or-probability-flux.html

  • Properties of the Eigenfunctions

    The eigenfunctions are the solutions of the eigenfunction equation the solutions for the one dimensional simple harmonic oscillator case, are polynomials in multiplied by a gaussian If the are normalized to unity they have the following properties: The...

    https://astarmathsandphysics.com/university-physics-notes/quantum-mechanics/1636-properties-of-the-eigenfunctions.html

  • Selection Rules for Transitions of Electrons Between Atomic Energy Levels

    In spectral phenomena such as the Zeeman it becomes evident that transitions are not observed between all pairs of energy levels. Some transitions are "forbidden" while others are "allowed" by a set of selection rules. That a...

    https://astarmathsandphysics.com/university-physics-notes/quantum-mechanics/1640-selection-rules-for-transitions-of-electrons-between-atomic-energy-levels.html

  • The Bohr Magnetron

    We can picture an electron in an atom moving in a circle of radius with speed The moving electron is equivalent to a current loop. A current loop with area and current has a magnetic dipole moment given by so for the electron above To find the current...

    https://astarmathsandphysics.com/university-physics-notes/quantum-mechanics/1645-the-bohr-magnetron.html

  • Compton Scattering

    Compton scattering is a type of scattering that X-rays and gamma rays undergo in matter. The elastic scattering – implying conservation of energy - of photons in matter results in a decrease in energy (increase in wavelength)of an X-ray or gamma ray...

    https://astarmathsandphysics.com/university-physics-notes/quantum-mechanics/1648-compton-scattering.html

  • The Infinite Square Well

    The infinite square well potential is given by: This is illustrated below. A particle under the influence of such a potential is free - no forces act - between and and is confined to that region by the need to have an infinite energy in order to travel...

    https://astarmathsandphysics.com/university-physics-notes/quantum-mechanics/1650-the-infinite-square-well.html

  • The Leonard - Jones Potential

    The Lennard-Jones or L-J potential is a mathematically simple model that describes the interaction between a pair of neutral atoms or molecules. The expression of the L-J potential is where is the depth of the potential well, is the (finite) distance...

    https://astarmathsandphysics.com/university-physics-notes/quantum-mechanics/1651-the-leonard-jones-potential.html

  • The Separation of Variables Method - The Simple Harmonic Oscillator

    In two dimensions Schrodinger's equation takes the form (1) Because x and y appear in the equation, we must assume is a function of both and If we assume that is a product of a function of with a function of then Substitution of this expression into...

    https://astarmathsandphysics.com/university-physics-notes/quantum-mechanics/1654-the-separation-of-variables-method-the-simple-harmonic-oscillator.html

  • The Stern Gerlach Experiment

    An electron, being a particle with an associated magnetic moment, may be pictured as a little spinning top. In the presence of a magnetic field this magnetic moment will align with the field in one of two ways – either spin up or spin down. The...

    https://astarmathsandphysics.com/university-physics-notes/quantum-mechanics/1656-the-stern-gerlach-experiment.html

  • The Weak Nuclear Force

    One of the four fundamental forces, about a million times weaker than the strong force – hence the name - the weak interaction involves the exchange of the intermediate vector bosons, the W and the Z. Since the mass of these particles is on the order...

    https://astarmathsandphysics.com/university-physics-notes/quantum-mechanics/1657-the-weak-nuclear-force.html

  • Summary of Quantum Numbers For Electrons in Atoms

    Solution of the Schrodinger Equation for the electron in the hydrogen atom gives rise to four quantum numbers. 1. The principal quantum number n. The allowed values of n are 1, 2, 3, 4, and so on. It may not be zero. This number along with the orbital...

    https://astarmathsandphysics.com/university-physics-notes/quantum-mechanics/1642-summary-of-quantum-numbers-for-electrons-in-atoms.html

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