Register to reply 
Operator in nonorthogonal basis 
Share this thread: 
#1
Oct407, 05:47 PM

P: 6

Hi, is possible make up a operator in a nonorthogonal basis, if is possible how I can contruct the operator.
thanks 


#2
Oct407, 08:26 PM

P: 701

why not form your operators as b><a



#3
Oct507, 10:11 AM

P: 6

which are the consequence of choice a basis nonorthogonal?



#4
Oct507, 11:25 AM

P: 46

Operator in nonorthogonal basis



#5
Oct507, 11:44 AM

Sci Advisor
HW Helper
P: 3,025

All you need to know is the effect of the operator on all the basis states. So if you know all the values of [itex] <a_iAa_j>[/itex] then you know everything about the operator. Alternatively, as quetzalcoatl9 pointed out, an arbitrary operators can be written as [itex] A = \sum c_{ij} a_i><a_j [/itex] One consequence of having a non orthonogonal basis is that you can't read off directly from the above expression what is the effect of applying the operator to a basis state gives. If the basis is orthogonal, then applying A to, say, [itex] a_3> [/itex] will simply give [itex] c_{13} a_1> + c_{23} a_2> + \ldots [/itex] (I am assuming that the labels of the states are discrete and start at 1). If the basis is not orthogonal, the expression is of course more complicated. 


#6
Oct507, 01:01 PM

P: 6

I can construct a basis depent of basis nonorthogonal, how might make up? and what happen with the eigenvalues and elements of the operator.
someone know if the situation present in some quantum system. 


Register to reply 
Related Discussions  
Inner products and orthogonal basis  Linear & Abstract Algebra  4  
Dot product of basis vectors in orthogonal coordinate systems  Calculus & Beyond Homework  5  
Orthogonal basis  Linear & Abstract Algebra  29  
Operator change of basis (QM / QI)  Linear & Abstract Algebra  6  
Orthogonal projection, orthonormal basis, coordinate vector of the polynomial?  Linear & Abstract Algebra  1 