Birth of Quantum Mechanics—Planck, Einstein, Bohr

2020 ◽  
pp. 81-99
Author(s):  
M. Suhail Zubairy
Keyword(s):  
Quantum Mechanics ◽  
Atomic Structure ◽  
Photoelectric Effect ◽  
Critical Value ◽  
Quantization Condition ◽  
Full Description ◽  
Max Planck ◽  
Foundation Of Quantum Mechanics ◽  
The Third

In this chapter, three problems whose resolution laid the foundation of quantum mechanics are discussed. First the pioneering work of Max Planck is described who explained the spectrum of light emitted from a so-called blackbody by making a bold ansatz that the energy associated with the oscillations of electrons comes in packets or quanta of energy. Second it is shown how Einstein invoked Planck’s hypothesis to explain the photoelectric effect by arguing that light should come in packets or quanta of energy and this energy should be proportional to the frequency. Electrons are emitted if the energy of the quantum of light, which has come to be known as a photon, is higher than a critical value. The third problem relates to the atomic structure of hydrogen. A full description is given of how Bohr applied a quantization condition to explain the emission of light at certain specific frequencies.

Quanta of the Third Kind

2021 ◽  
Vol 6 (3) ◽  
Author(s):  
Frank Wilczek
Keyword(s):  
Quantum Mechanics ◽  
Experimental Results ◽  
Quantum Mechanical ◽  
The Third

Quantum mechanics is nearly one hundred years old; and yet the challenge it presents to the imagination is so great that scientists are still coming to terms with some of its most basic implications. Theoretical insights and recent experimental results in anyon physics are leading physicists to revise and expand their ideas about what quantum-mechanical particles are and how they behave.

Philosophy of Quantum Mechanics: Dynamical Collapse Theories

2021 ◽  
Author(s):  
Angelo Bassi
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
New Technologies ◽  
Stochastic Dynamics ◽  
Laws Of Nature ◽  
Nonlinear Effects ◽  
Foundation Of Quantum Mechanics ◽  
Quantum Phenomena ◽  
The One ◽  
Collapse Theories

Quantum Mechanics is one of the most successful theories of nature. It accounts for all known properties of matter and light, and it does so with an unprecedented level of accuracy. On top of this, it generated many new technologies that now are part of daily life. In many ways, it can be said that we live in a quantum world. Yet, quantum theory is subject to an intense debate about its meaning as a theory of nature, which started from the very beginning and has never ended. The essence was captured by Schrödinger with the cat paradox: why do cats behave classically instead of being quantum like the one imagined by Schrödinger? Answering this question digs deep into the foundation of quantum mechanics. A possible answer is Dynamical Collapse Theories. The fundamental assumption is that the Schrödinger equation, which is supposed to govern all quantum phenomena (at the non-relativistic level) is only approximately correct. It is an approximation of a nonlinear and stochastic dynamics, according to which the wave functions of microscopic objects can be in a superposition of different states because the nonlinear effects are negligible, while those of macroscopic objects are always very well localized in space because the nonlinear effects dominate for increasingly massive systems. Then, microscopic systems behave quantum mechanically, while macroscopic ones such as Schrödinger’s cat behave classically simply because the (newly postulated) laws of nature say so. By changing the dynamics, collapse theories make predictions that are different from quantum-mechanical predictions. Then it becomes interesting to test the various collapse models that have been proposed. Experimental effort is increasing worldwide, so far limiting values of the theory’s parameters quantifying the collapse, since no collapse signal was detected, but possibly in the future finding such a signal and opening up a window beyond quantum theory.

No-cloning Theorem and Quantum Copying

2020 ◽  
pp. 172-181
Author(s):  
M. Suhail Zubairy
Keyword(s):  
Quantum Mechanics ◽  
Quantum State ◽  
Uncertainty Relation ◽  
Foundations Of Quantum Mechanics ◽  
Quantum Cloning ◽  
Foundation Of Quantum Mechanics ◽  
Quantum Copying ◽  
Arbitrary Quantum ◽  
Principle Of Complementarity

Heisenberg’s uncertainty relation and Bohr’s principle of complementarity form the foundations of quantum mechanics. If these are violated then the edifice of quantum mechanics can come crashing down. In this chapter, it is shown how cloning or perfect copying of a quantum state can potentially lead to a violation of these sacred principles. A no-cloning theorem is proven showing that the cloning of an arbitrary quantum state is not allowed. The foundation of quantum mechanics is therefore protected. It is also shown how quantum cloning can lead to superluminal communication. It is also discussed that, if making a perfect copy of a quantum state is forbidden, how best a copy of a state can be made.

Coupling coefficients and tensor operators for chains of groups

1975 ◽  
Vol 277 (1272) ◽  
pp. 545-585 ◽  
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Group Theory ◽  
Linear Operators ◽  
Coupling Coefficients ◽  
Vector Representation ◽  
General Statement ◽  
The Third ◽  
Representation Spaces ◽  
Definition Of

The action of an arbitrary (but finite or compact) group on an arbitrary Hilbert space is studied. The application of group theory to physical calculations is often based on the Wigner-Eckart theorem, and one of the aims is to lead up to a general proof of this theorem. The group’s action gives irreducible ket-vector representation spaces, products of which lead to a definition of coupling (Wigner, or Clebsch-Gordan) coefficients and jm and j symbols. The properties of these objects are studied in detail, beginning with properties that are independent of the basis chosen for the representation spaces. We then explore some of the consequences of choosing bases by using the action of a subgroup. This leads to the Racah factorization lemma and the definition of jm factors, also a general statement of Racah’s reciprocity. In the third part, we add to these ideas, some properties of the space of all linear operators taking the Hilbert space to itself. This leads to a proof of the Wigner—Eckart theorem which is both succinct and in the language of quantum mechanics.

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