New derivation of pi links quantum physics and pure math

In 1655 the English mathematician John Wallis published a book in which he derived a formula for pi as the product of an infinite series of ratios. Now researchers from the University of Rochester, in a surprise discovery, ...

Physicist proves impossibility of quantum time crystals

(Phys.org) —Is it possible that a moving object could have zero energy? The common sense answer is no, since motion itself is kinetic energy, but this answer has been challenged recently by the concept of quantum time crystals. ...

Theorists solve a long-standing fundamental problem

Trying to understand a system of atoms is like herding gnats - the individual atoms are never at rest and are constantly moving and interacting. When it comes to trying to model the properties and behavior of these kinds ...

Creating time crystals with a rotating ion ring

(Phys.org) —There has been a lot of talk recently about the possibility of building what has come to be known as a time crystal. In February 2012, Frank Wilczek originally proposed the idea that under certain conditions, ...

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Energy level

A quantum mechanical system or particle that is bound, confined spatially, can only take on certain discrete values of energy, as opposed to classical particles, which can have any energy. These values are called energy levels. The term is most commonly used for the energy levels of electrons in atoms or molecules, which are bound by the electric field of the nucleus. The energy spectrum of a system with energy levels is said to be quantized.

If the potential energy is set to zero at infinity, the usual convention, then bound electron states have negative potential energy.

Energy levels are said to be degenerate, if the same energy level is obtained by more than one quantum mechanical state. They are then called degenerate energy levels.

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