{"product_id":"a-mathematical-journey-to-quantum-salvatore-capozziello-9783030861001","title":"A Mathematical Journey to Quantum Mechanics","description":"1 Newtonian Mechanics, Lagrangians and Hamiltonians 151.1 Some Words about the Priciples of Newtonian Mechanics . . . . . . . . . . . . 151.2 The Mechanical Lagrangian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171.3 Lagrangians and Euler-Lagrange Equations . . . . . . . . . . . . . . . . . . . . 211.4 The Mechanical Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241.5 Hamiltonians and General Hamilton's Equations . . . . . . . . . . . . . . . . . 271.6 Poisson's Brackets in Hamiltonian Mechanics . . . . . . . . . . . . . . . . . . . 29\u003cbr\u003e2 Can Light Be Described by Classical Mechanics? 332.1 Michelson-Morley Experiment and the Principles of Special Relativity . . . . . 332.2 Moving among Inertial Frames: Lorentz Transformations . . . . . . . . . . . . 382.3 Addition of Velocities: the Relativistic Formula . . . . . . . . . . . . . . . . . . 412.4 Einstein's Rest Energy Formula: E=mc2 . . . . . . . . . . . . . . . . . . . . . 422.5 Relativistic Energy Formula: E2 = p2 c2 + m2 c4 . . . . . . . . . . . . . . . . . 442.6 Describing Electromagnetic Waves: Maxwell's Equations . . . . . . . . . . . . . 442.7 Invariance under Lorentz Transformations and non-Invariance under Galilei'sTransformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48\u003cbr\u003e3 Why Quantum Mechanics? 513.1 What Do We Think about the Nature of Matter . . . . . . . . . . . . . . . . . 513.2 Monochromatic Plane Waves - the One Dimensional Case . . . . . . . . . . . . 553.3 Young's Double Split Experiment: Light Seen as a Wave . . . . . . . . . . . . . 603.4 The Plank-Einstein formula: E=hf . . . . . . . . . . . . . . . . . . . . . . . . . 643.5 Light Seen as a Corpuscle: Einstein's Photoelectric Eect . . . . . . . . . . . . 693.6 Atomic Spectra and Bohr's Model of Hydrogen Atom . . . . . . . . . . . . . . . 703.7 Louis de Broglie Hypothesis: Material Objects Exhibit Wave-like Behavior . . . 733.8 Strengthening Einstein's Idea: The Compton Eect . . . . . . . . . . . . . . . . 75\u003cbr\u003e4 Schringer's Equations and Consequences 794.1 The Schringer's Equations - the one Dimensional Case . . . . . . . . . . . . . 794.2 Solving Schringer Equation for the Free Particle . . . . . . . . . . . . . . . . 814.3 Solving Schringer Equation for a Particle in a Box . . . . . . . . . . . . . . . 824.4 Solving Schringer Equation in the Case of Harmonic Oscillator. The Quantified Energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85\u003cbr\u003e5 The Mathematics behind the Harmonic Oscillator 915.1 Hermite Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 915.2 Real and Complex Vector Structures . . . . . . . . . . . . . . . . . . . . . . . . 975.2.1 Finite Dimensional Real and Complex Vector Spaces, Inner Product, Norm, Distance, Completeness . . . . . . . . . . . . . . . . . . . . . . . 975.2.2 Pre-Hilbert and Hilbert Spaces . . . . . . . . . . . . . . . . . . . . . . . 1005.2.3 Examples of Hilbert Spaces . . . . . . . . . . . . . . . . . . . . . . . . . 1035.2.4 Orthogonal and Orthonormal Systems in Hilbert Spaces . . . . . . . . . 1095.2.5 Linear Operators, Eigenvalues, Eigenvectors and Schringer Equation . 1105.3 Again about de Broglie Hypothesis: Wave-Particle Duality and Wave Packets . 1155.4 More about Electron in an Atom . . . . . . . . . . . . . . . . . . . . . . . . . . 118\u003cbr\u003e6 Understanding Heisenberg's Uncertainty Principl\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Salvatore Capozziello, Wladimir-Georges Boskoff\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 3030861007\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9783030861001\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 09\/29\/2022\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 289\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.96lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.21h x 6.14w x 0.65d","brand":"Salvatore Capozziello","offers":[{"title":"Paperback","offer_id":44072557183231,"sku":"9783030861001","price":64.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_5dbc7971-6e65-44cd-9982-add885e0db6d.jpg?v=1685442683","url":"https:\/\/www.whiterainbookhouse.com\/products\/a-mathematical-journey-to-quantum-salvatore-capozziello-9783030861001","provider":"WR Book House","version":"1.0","type":"link"}