Bra–ket notation, also called Dirac notation, is a notation for linear algebra and linear operators on complex vector spaces together with their dual space both in the finite-dimensional and infinite-dimensional case. It is specifically designed to ease the types of calculations that frequently come up in quantum mechanics.

2023年7月2日 · Bra-Ket 符号 （Bra-Ket Notation），也被称为 Dirac 符号，是量子力学中一种表达矢量和矩阵元素的强大工具。 其名字来源于拆分英文单词'Bracket'，表达了这个符号的图形特性。 在量子物理中， 这种符号用于描绘抽象的 希尔伯特空间 中的向量和操作，为理解和操作量子态提供了一种清晰、紧凑的方式。 在接下来的讨论中，我们将深入探索Bra-Ket符号的细节以及它如何在量子力学中被使用。 考虑一个一维的波函数Ψ (X)，描述一个量子力学粒子。 在点X_1处的 …

It is convenient to employ the Dirac symbol j i, known as a \ket", to denote a quantum state without referring to the particular function used to represent it. The kets, which we shall also refer to as vectors to distinguish them from scalars, which are complex numbers, are the elements of the quantum Hilbert space H.

作为内积的推广, 我们定义 \mathscr H 上的 共轭双线性泛函 为 \mathscr H\times\mathscr H\to\mathbb C 的映射, 其对第一个元素是线性的, 对第二个元素是共轭线性的.

Bra-Ket is a way of writing special vectors used in Quantum Physics that looks like this: Here is a vector in 3 dimensions: We can write this as a column vector like this: Or we can write it as a "ket": But kets are special: Kets can have any number of …

2010年2月4日 · A quantum state is represented by the ket |ψi. The Hermitian conjugate is the bra hψ|. The inner product is hφ|ψi = c (a number). If c = hφ|ψi then the complex conjugate is c∗ = hφ|ψi∗ = hψ|φi. Kets and bras exist in.

For every ket, there’s a corresponding bra. (The terms come from bra-ket, or bracket.) A bra is the Hermitian conjugate of the corresponding ket. Suppose you start with this ket: The asterisk (*) symbol in the following equation means the complex conjugate.

2022年5月22日 · Kets, bras, brackets and operators are the building bricks of bracket notation, which is the most commonly used notation for quantum mechanical systems. They can be thought of as column vectors, row vectors, dot products and matrices respectively.

2016年5月10日 · In short terms, kets are vectors on your Hilbert space, while bras are linear functionals of the kets to the complex plane. |ψ ∈ H. ϕ|: H → C |ψ ↦ ϕ | ψ . Due to the Riesz-Frechet theorem, a correspondence can be established between H and the space of linear functionals where the bras live, thereby the maybe slightly ambiguous notation.

The ket is an abstract quantity that represents a quantum state. Often, we wish to be more specific an explicit representation that gives us information about (for example) spatial (position) distribution of electron density. To do this, we “project” the ket onto the bras that are the eigenstates of position.