What Are the Key Concepts of Quantum Theory?

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Quantum theory posits that energy exists in discrete units called "quanta," similar to the ancient concept of atoms. It asserts that particles can occupy multiple states simultaneously, a principle known as superposition. The observer effect indicates that measuring a particle can alter its behavior, while the uncertainty principle highlights the impossibility of simultaneously knowing a particle's exact position and momentum. This framework has fundamentally transformed our understanding of physics and has significant implications for technology and computing. Quantum theory remains a cornerstone of modern scientific inquiry.
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dear reader,
could anyone say what is quantum theory exactly??[?] [?]
 
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At its most basic level, QT is the theory that energy, and therefore most everything, comes in discrete packages, or "quanta", the same root from which we get our modern word "quantity". Like the ancient Greek idea of the "atom", these energy packages are believed to be indivisible. For example, the quanta for EM energy is the photon. Quantum theory states that an atom infused with enough energy to emit a single photon will do so, but that same atom, given slightly less energy, will not emit one-half of a photon.
 


Quantum theory is a fundamental framework in physics that explains the behavior of particles at a microscopic level. It is based on the idea that particles, such as atoms and subatomic particles, can exist in multiple states or positions simultaneously. This is known as the principle of superposition. Additionally, the theory also states that the act of observing or measuring a particle can affect its behavior, known as the observer effect. This theory also includes the concept of uncertainty, which states that it is impossible to know both the position and momentum of a particle with absolute certainty. Overall, quantum theory has revolutionized our understanding of the universe and has many practical applications, such as in computing and technology.
 
Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?

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