VitorMSAlmeida.pt

Once again, I read nonsense about quantum physics, and in this case on a social network by a “guru” at a festival that just ended yesterday.

I had already criticized this type of person before, because of their methods (use of psychotropic drugs), their teachings (points detached from occultism and without coherence), and for trying, through errors of total ignorance and stupidity, to use physics as an argument.

So, here is a brief and simple explanation of what quantum mechanics is:

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Quantum mechanics describes the behavior of matter and energy at atomic and subatomic scales. It replaces classical mechanics with a probabilistic framework based on wave functions, operators, and discrete spectra. Classical physics fails for phenomena such as blackbody radiation, the photoelectric effect, atomic spectra, and electron diffraction; quantum mechanics accounts for them quantitatively.

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Core Principles

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Wave-particle duality
Matter and radiation exhibit both particle-like and wave-like properties. Photons carry energy $E=hν$ and momentum p=h/λ
(Planck’s relation). Particles such as electrons have an associated de Broglie wavelength λ=h/p. Interference and diffraction experiments confirm the wave aspect; discrete detection events confirm the particle aspect.

Quantization
Certain observables take only discrete values. Energy levels of bound systems (atoms, harmonic oscillators, particles in a box) are quantized. Angular momentum components are quantized in units of ℏ=h/2π. This discreteness follows from the requirement that wave functions be single-valued and normalizable, or from the algebraic structure of the corresponding operators.

Heisenberg uncertainty principle
Incompatible observables cannot be simultaneously sharp. The most famous form is Δx Δpx≥ℏ/2, where Δx and Δpx are standard deviations. Analogous relations hold for energy and time, and for angular-momentum components. The principle is a direct consequence of the non-commutativity of the corresponding operators ([x,px]=iℏ).

Superposition
If ∣ψ1⟩ and ∣ψ2⟩ are possible states, any linear combination ∣ψ⟩=c1∣ψ1⟩+c2∣ψ2⟩ (with complex coefficients) is also a possible state. Measurement yields one of the component outcomes with probabilities given by the Born rule. Superposition produces interference; the classic two-slit experiment with single particles demonstrates this.

Probabilistic interpretation (Born rule)
The state of a system is completely described by a normalized wave function ψ(r,t) (or, more abstractly, a state vector in Hilbert space). The probability density of finding the particle at position r is ∣ψ(r,t)∣2| . For a general observable (A) with eigenstates ∣a⟩ , the probability of obtaining eigenvalue (a) is ∣⟨a∣ψ⟩∣2|.

Measurement and state update
An ideal measurement of an observable yields one of its eigenvalues and projects the state onto the corresponding eigenspace (wave-function “collapse” in the Copenhagen formulation). Subsequent measurements of the same observable yield the same result if the system is not otherwise disturbed.

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Mathematical Framework

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State space
Pure states are rays in a complex Hilbert space H . Composite systems are described by the tensor product of the individual Hilbert spaces. Mixed states are density operators ρ (positive, trace-1 operators).

Observables
Physical quantities are represented by Hermitian (self-adjoint) operators. The possible measurement outcomes are the eigenvalues of the operator. Expectation values are ⟨A⟩=⟨ψ∣A∣ψ⟩ (or Tr⁡(ρA) for mixed states).

Time evolution
In the Schrödinger picture the state evolves unitarily according to the time-dependent Schrödinger equation
iℏ.∂/∂t∣ψ(t)⟩=H∣ψ(t)⟩,

where (H) is the Hamiltonian operator. Equivalently, the time-evolution operator is $U(t) = e^{-iHt/\hbar}$ (for time-independent (H)). The Schrödinger equation is linear and preserves the norm, guaranteeing probability conservation.

Stationary states
When (H) is time-independent, energy eigenstates satisfy the time-independent Schrödinger equation
Hψ=Eψ.

These states have definite energy and acquire only a global phase e−iEt/ℏe^{-iEt/\hbar}e^{-iEt/\hbar}
under time evolution.

Spin and identical particles
In addition to orbital degrees of freedom, particles possess intrinsic spin. Fermions (half-integer spin) obey the Pauli exclusion principle and are described by antisymmetric wave functions; bosons (integer spin) are described by symmetric wave functions. This underlies the structure of the periodic table and the statistics of quantum gases.

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Important Consequences and Phenomena

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– Quantum tunneling: A particle can penetrate a classically forbidden region with non-zero probability.
– Entanglement: The joint state of two or more particles cannot be written as a product of individual states. Measurement outcomes are correlated more strongly than any classical local-hidden-variable theory allows (Bell inequalities).
– Discrete spectra and selection rules: Atomic and molecular spectroscopy.
– Zero-point energy: Even the ground state of a harmonic oscillator has energy 1/2ℏω.

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Postulates (compact statement)

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1. The state is a normalized vector (or density operator) in Hilbert space.
2. Observables are Hermitian operators; measurement outcomes are eigenvalues.
3. Probabilities are given by the Born rule.
4. Between measurements the state evolves unitarily via the Schrödinger equation.
5. Immediately after an ideal measurement the state is the corresponding eigenstate (projection postulate).

These principles, together with the specific form of the Hamiltonian for a given system, constitute the predictive core of non-relativistic quantum mechanics. Relativistic extensions (Dirac equation, quantum field theory) incorporate special relativity and particle creation/annihilation while retaining the same probabilistic and operator structure.
The theory is experimentally confirmed to extremely high precision in atomic physics, quantum optics, condensed-matter systems, and particle physics. Interpretational questions (the measurement problem, the ontological status of the wave function) remain active areas of foundational research, but they do not alter the operational rules used for calculations and predictions.

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Conclusions:

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I hope this has helped. For easy and comprehensive reading, I highly recommend Brian Greene’s “The Elegant Universe,” which requires no prior mathematical knowledge.

Despite studying physics (my academic background) and having studiednd practiced occultism for decades, I don’t consider myself capable of “selling”/deceiving with the limited knowledge I possess. Worse still, is the practice of selling and spreading this same nonsense to people thirsty for knowledge who are easily deceived.

But that’s not what we see every day in professional politicians and their cronies and dependents.