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j_dirac
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Hi, is possible make up a operator in a non-orthogonal basis, if is possible how I can contruct the operator.
thanks
thanks
j_dirac said:which are the consequence of choice a basis non-orthogonal?
j_dirac said:Hi, is possible make up a operator in a non-orthogonal basis, if is possible how I can contruct the operator.
thanks
An operator in a non-orthogonal basis is a mathematical representation of a physical quantity, such as position or momentum, in a system with non-orthogonal basis vectors. This means that the basis vectors for the system are not perpendicular to each other, making it more difficult to define and manipulate operators.
Operators in non-orthogonal bases are more complex and difficult to work with compared to those in orthogonal bases. This is because in a non-orthogonal basis, the basis vectors are not perpendicular to each other, making it more challenging to define and manipulate operators. In an orthogonal basis, the basis vectors are perpendicular, making it easier to define and manipulate operators.
One of the main challenges of working with operators in non-orthogonal bases is that they do not commute with each other, meaning that the order in which they are applied matters. Additionally, the inner product of two states in a non-orthogonal basis is not simply the product of their components, making calculations more complex.
In quantum mechanics, operators in non-orthogonal bases are used to represent physical quantities, such as energy and momentum, in a system with non-orthogonal basis vectors. They are also used in calculations to determine the probability of a particle being in a certain state or location.
Yes, operators in non-orthogonal bases can be transformed into operators in an orthogonal basis using a mathematical process called basis transformation. This involves finding a transformation matrix that can convert the non-orthogonal basis vectors into orthogonal ones, and then applying this transformation to the operators. This makes it easier to work with the operators and perform calculations in quantum mechanics.