caret
Explanation:
Such a conversion results from the change-of-basis formula which expresses the coordinates relative to one basis in terms of coordinates relative to the other basis. Using matrices, this formula can be written
xold = Axnew
where "old" and "new" refer respectively to the firstly defined basis and the other basis, and xnew are the column vectors of the coordinates of the same vector on the two bases, and is the change-of-basis matrix (also called transition matrix), which is the matrix whose columns are the coordinate vectors of the new basis vectors on the old basis.
https://en.wikipedia.org/wiki/Change_of_basis
In computing, the caret is the name used familiarly of the character ^, the 'freestanding' circumflex, provided on QWERTY keyboards using ↑ Shift+6. The symbol has a variety of uses in programming and mathematics.
:
In mathematics, the caret can signify exponentiation (3^5 for 35), where the usual superscript is not readily usable (as on some graphing calculators).
https://en.wikipedia.org/wiki/Caret_(computing)
If the vector of response values is denoted by y and the vector of fitted values by ŷ = Py
As ŷ is usually pronounced "y-hat", the projection matrix P is also named hat matrix as it "puts a hat on y".
https://en.wikipedia.org/wiki/Projection_matrix
Stationary states can also be described by a simpler form of the Schrödinger equation, the time-independent Schrödinger equation.
Time-independent Schrödinger equation (general)
Ĥ | Ψ > = E | Ψ >
where E is the energy of the system.
:
Unitarity
Further information: Wigner's theorem
Holding the Hamiltonian Ĥ constant, the Schrödinger equation has the solution … [formula
:
Changes of basis
The Schrödinger equation is often presented using quantities varying as functions of position, but as a vector-operator equation it has a valid representation in any arbitrary complete basis of kets in Hilbert space. As mentioned above, "bases" that lie outside the physical Hilbert space are also employed for calculational purposes.
https://en.wikipedia.org/wiki/Schrödinger_equation
Da "caret" im Kontext wesentlich häufiger als "hat" verwendet wird, schlage ich diese Schreibweise vor, vor allem im Hinblick auf die Zielgruppe, die vermutlich kein einschlägiges Studium der Physik oder Mathematik absolviert hat.
caret [COMP.] | der Zirkumflex Pl.: die Zirkumflexe
caret [COMP.] | das Caret-Zeichen
https://dict.leo.org/englisch-deutsch/caret
Hinweis, die mit Caret gekrönten Buchstaben findet man auch in der Windows-Zeichentabelle.
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Note added at 2 hrs (2022-05-27 12:49:48 GMT)
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The Chemical Bond: A Fundamental Quantum-Mechanical Picture
:
The symbol Ĥ in 1.1 is called the Hamilton operator Hammiltonian, and stands for a mathematical manipulation. While a general explanation of such manipulations will be giben in Chap. 2, for thsi simple exampe, we can tak Ĥ to be equal to a constan timest he second derivatit of Φ(x) with respect to x, i.e., Ĥ = -ħ²/2me) x (d²/dx²).Here , the symbol ħ means ħ = h / ( 24 ) , and the caret is to emphasize that Ĥ is an operator.
https://books.google.de/books?id=eYSDtZxH8ZgC&pg=PA4&lpg=PA4...
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Note added at 3 hrs (2022-05-27 13:45:55 GMT)
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Den Text konnte ich nicht kopieren, sondern musste ihn abschreiben und die Sonderzeichen von Hand einfügen. Deshalb sind mir ein paar Tippfehler unterlaufen, die ich hiermit korrigiere:
The symbol Ĥ in 1.1 is called the Hamilton operator Hammiltonian, and stands for a mathematical manipulation. While a general explanation of such manipulations will be given in Chap. 2, for this simple example, we can take Ĥ to be equal to a constant times he second derivative of Φ(x) with respect to x, i.e., Ĥ = -ħ²/2me) x (d²/dx²).Here, the symbol ħ means ħ = h/(2π), and the caret is to emphasize that Ĥ is an operator.
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Note added at 3 hrs (2022-05-27 13:48:16 GMT)
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Nochmal (the statt he):
The symbol Ĥ in 1.1 is called the Hamilton operator Hammiltonian, and stands for a mathematical manipulation. While a general explanation of such manipulations will be given in Chap. 2, for this simple example, we can take Ĥ to be equal to a constant times the second derivative of Φ(x) with respect to x, i.e., Ĥ = -ħ²/2me) x (d²/dx²).Here, the symbol ħ means ħ = h/(2π), and the caret is to emphasize that Ĥ is an operator.
| Johannes Gleim
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