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u/hongooi 4d ago
c2m = E - IA
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u/randomdreamykid 4d ago
VP=TnR
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u/WanderingWrackspurt 4d ago
now write the Schrodinger eq this way 😭
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u/EconomicSeahorse Student 3d ago
One time I actually saw (a completely unironic) ∂²ψ/∂x² + 8π²m/h²•(E - V)ψ = 0 😭
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u/Zannis250 4d ago
Hot take: F=am is miles better than F=ma. If you are writing by hand the transition from a to m is seamless while from m to a is weird
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u/djjddjjd9753 4d ago
What does it mean? Could someone explain the last equation?
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u/Grand_Protector_Dark 4d ago
The joke is simply that these relationships are written in a non standard form, making it look "weird".
F = a m , usually written as F = m a,
Newton's second law of motion, equating the force acting on an object with the mass experiencing an acceleration.c2 m = E, usually written as E = m c2
The mass - energy equivalence. All mass that exists and is at rest (stationary) still contains an Intrinsic energy.T-1 π2, usually written as 2π T-1 = ω or 2πf = ω
T is the time period, the time it takes for a repeating process to repeat once. f is frequency, how many times per time interval (usually per second) something will occur.
Cyclical patterns can be represented as a pointer rotating around a circle. That pointer can be represented as the angle it makes with the x axis. The angular frequency is the angle per unit time or rate of change of that angles (how fast the angle changes).
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u/DiscoPotato69 4d ago
All fun and games until things are no longer Newtonian and Operators and Indices and Matrices just start driving you insane
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u/Limp-Field5075 4d ago
Quantum mechanics is a cornerstone of modern physics, exploring the behavior of matter and light at the atomic and subatomic levels. Unlike classical physics, which describes the macroscopic world, quantum mechanics reveals a fundamentally different reality at the smallest scales, where particles exhibit both wave-like and particle-like properties, a phenomenon known as wave-particle duality. Here's a breakdown of key aspects in a complex manner: 1. Wave-particle duality and the wavefunction Duality: Quantum objects, such as electrons and photons, don't behave as either waves or particles exclusively, but rather exhibit characteristics of both depending on the observation. This means that describing them as either a classical particle or a classical wave is insufficient. Wavefunction (Ψ): In quantum mechanics, the state of a particle is described by a mathematical function called the wavefunction, Ψ. This complex-valued function contains all the accessible information about the system. Born Interpretation: The square of the magnitude of the wavefunction, |Ψ|², represents the probability density of finding the particle at a given location in space and time. This inherently probabilistic nature is a departure from the deterministic world of classical physics Normalization: For bound particles, the wavefunction is typically normalized, meaning the integral of |Ψ|² over all space equals 1, reflecting the certainty of finding the particle somewhere. 2. The Schrödinger equation: governing the evolution Equation of Motion: For non-relativistic quantum mechanics, the evolution of the wavefunction over time is governed by the Schrödinger equation, a linear partial differential equation. Hamiltonian Operator: The equation involves the Hamiltonian operator, Ĥ, which represents the total energy of the system and acts upon the wavefunction. Time-independent and Time-dependent: The Schrödinger equation can be expressed in time-dependent and time-independent forms. The time-independent form is used to find stationary states with defined energies. Quantization: Solving the Schrödinger equation for a given system reveals the possible energy levels of the system, which are often quantized, meaning they can only take on discrete values, unlike the continuous energy spectrum seen in classical physics. 3. Relativistic considerations: the Dirac equation and beyond Limitations of Schrödinger Equation: The Schrödinger equation is non-relativistic and thus doesn't fully account for particles moving at speeds approaching the speed of light. Dirac Equation: To incorporate special relativity into quantum mechanics, Paul Dirac formulated the Dirac equation in 1928. This relativistic wave equation describes spin-1/2 particles, such as electrons and quarks. Spin and Antiparticles: The Dirac equation naturally explains the intrinsic angular momentum of electrons, known as spin, and predicted the existence of antiparticles, like the positron, before their experimental discovery. Quantum Field Theory: The impermanence of matter suggested by the Dirac theory led to the development of quantum field theory (QFT), where particles are seen as excitations in various quantum fields that permeate spacetime. 4. Quantum field theory: a unified framework Unification: QFT combines quantum mechanics, special relativity, and classical field theory into a single theoretical framework. Fields as Fundamental: In QFT, fundamental particles are not viewed as independent entities but rather as excitations or quanta of underlying quantum fields. Force Carriers: Interactions between particles are explained through the exchange of force-carrying bosons, such as photons for the electromagnetic force or gluons for the strong force. Standard Model: QFT forms the foundation of the Standard Model of particle physics, which describes the electromagnetic, weak, and strong interactions, and all known elementary particles. Beyond the Standard Model: Despite its successes, the Standard Model doesn't incorporate gravity or fully explain phenomena like dark matter and neutrino oscillations, prompting ongoing research into physics beyond the Standard Model. In essence, quantum mechanics, particularly through its advanced formulations like Quantum Field Theory, provides the most comprehensive description of the fundamental building blocks of the universe and their interactions, albeit with remaining mysteries to unravel.
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u/IhtiramKhan 4d ago
Ew, this just feels wrong.