Lecture

Hydrogen-like Atom: Quantum Mechanics

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In course

MICRO-530: Nanotechnology

This course gives the basics for understanding nanotechnology from an engineer's perspective: physical background, materials aspects and scaling laws, fabrication and imaging of nanoscale devices. ...

Description

This lecture covers the theoretical aspects of the hydrogen-like atom, including the time-independent Schrödinger equation, solutions in spherical coordinates, energy operators, quantum numbers, and orbital representations. It delves into the complex eigenfunctions and simple eigenvalues of the atom, providing insights into its energy levels and angular momentum operators.

Instructors (2)

Giovanni Boero

Expertise Nuclear magnetic resonance (NMR), Electron spin resonance (ESR), Ferromagnetic resonance (FMR), RF/MW discrete and integrated electronics, Magnetic sensors, Noise phenomena. Mission Methods based on the magnetic resonance of nuclear spins (nuclear magnetic resonance (NMR)), unpaired electrons spins (electron spin resonance (ESR)), and coupled electron spins electrons (ferromagnetic resonance (FMR)) are very powerful radiofrequency/microwave spectroscopy tools used in many research and industrial a

Jürgen Brugger

I am a Professor of Microengineering and co-affiliated to Materials Science. Before joining EPFL I was at the MESA Research Institute of Nanotechnology at the University of Twente in the Netherlands, at the IBM Zurich Research Laboratory, and at the Hitachi Central Research Laboratory, in Tokyo, Japan. I received a Master in Physical-Electronics and a PhD degree from Neuchâtel University, Switzerland. Research in my laboratory focuses on various aspects of MEMS and Nanotechnology. My group contributes to the field at the fundamental level as well as in technological development, as demonstrated by the start-ups that spun off from the lab. In our research, key competences are in micro/nanofabrication, additive micro-manufacturing, new materials for MEMS, increasingly for wearable and biomedical applications. Together with my students and colleagues we published over 200 peer-refereed papers and I had the pleasure to supervise over 25 PhD students. Former students and postdocs have been successful in receiving awards and starting their own scientific careers. I am honoured for the appointment in 2016 as Fellow of the IEEE “For contributions to micro and nano manufacturing technology”. In 2017 my lab was awarded an ERC AdvG in the field of advanced micro-manufacturing.

Official source

Ontological neighbourhood

Physics

Atomic physics: Topics in atomic physics

Related concepts (32)

Angular momentum operator

In quantum mechanics, the angular momentum operator is one of several related operators analogous to classical angular momentum. The angular momentum operator plays a central role in the theory of atomic and molecular physics and other quantum problems involving rotational symmetry. Such an operator is applied to a mathematical representation of the physical state of a system and yields an angular momentum value if the state has a definite value for it.

Azimuthal quantum number

In quantum mechanics, the azimuthal quantum number is a quantum number for an atomic orbital that determines its orbital angular momentum and describes the shape of the orbital. The azimuthal quantum number is the second of a set of quantum numbers that describe the unique quantum state of an electron (the others being the principal quantum number n, the magnetic quantum number m_l, and the spin quantum number m_s). It is also known as the orbital angular momentum quantum number, orbital quantum number, subsidiary quantum number, or second quantum number, and is symbolized as l (pronounced ell).

Angular momentum

In physics, angular momentum (sometimes called moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity – the total angular momentum of a closed system remains constant. Angular momentum has both a direction and a magnitude, and both are conserved. Bicycles and motorcycles, flying discs, rifled bullets, and gyroscopes owe their useful properties to conservation of angular momentum.

Quantum number

In quantum physics and chemistry, quantum numbers describe values of conserved quantities in the dynamics of a quantum system. Quantum numbers correspond to eigenvalues of operators that commute with the Hamiltonian—quantities that can be known with precision at the same time as the system's energy—and their corresponding eigenspaces. Together, a specification of all of the quantum numbers of a quantum system fully characterize a basis state of the system, and can in principle be measured together.

Principal quantum number

In quantum mechanics, the principal quantum number (symbolized n) is one of four quantum numbers assigned to each electron in an atom to describe that electron's state. Its values are natural numbers (from 1) making it a discrete variable. Apart from the principal quantum number, the other quantum numbers for bound electrons are the azimuthal quantum number l, the magnetic quantum number ml, and the spin quantum number s. As n increases, the electron is also at a higher energy and is, therefore, less tightly bound to the nucleus.

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