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Is the complex conjugate to the outer product this? :
( |a> <b| ) * = ( |b> <a| )
?
( |a> <b| ) * = ( |b> <a| )
?
malawi_glenn said:so
(<a|b>) * = (<b|a>)
but not
( |a> <b| ) * = ( |b> <a| )
?
A Bra Ket is a mathematical notation used in quantum mechanics to represent a vector in a complex vector space. It is a combination of the terms "bra" and "ket", where "bra" represents the conjugate transpose of a vector and "ket" represents a vector itself.
An outer product is a mathematical operation that takes two vectors and produces a matrix. It is also known as a tensor product and is commonly used in linear algebra and quantum mechanics.
A complex conjugate is a mathematical operation that involves changing the sign of the imaginary component of a complex number. For example, the complex conjugate of 3+4i is 3-4i.
In quantum mechanics, the Bra Ket notation is used to represent the state of a quantum system. The bra vector represents the conjugate transpose of the state vector , and the outer product is used to represent a projection operator onto that state.
The Bra Ket notation is useful in quantum mechanics because it allows for a concise representation of complex vector spaces and operators. It also follows the principles of linear algebra, making it easier to perform calculations and understand the behavior of quantum systems.