2- prove that this function 4 = Ae-ax Is an Eigenfunction for this operator d? 2 d + x dx 2a dx? Where A and a are constants.

Q: H6

A: For Anti-hermitian,  A^,B^+=-A^,B^ So, B^+A^+-A^+B^+=B^A^-A^B^ This condition is only possible when…

Q: Q2. If you are given the following operator 03, acts on function of position (x). as: 034(x) = ¥(x)…

A:

Q: 2 ô Consider operator Ô 1 and function R(r)= e br. What must be the r ôr value of constant b for…

A: The operator is given as, O^=-∂2∂r2+2r∂∂r-1r The function is given as, R(r)=e-br Applying the…

Q: Q2. If you are given the following operator 03, acts on function of position 4(x). as: O34(x) = v(x)…

A: Given, O3 and OT are the operators, And when they operate on function ψx then…

Q: 16. If A and B are Hermitian operators and [A, B] = o, then they share 17. It is common to label…

A: If A and B are Hermitian operators and [A, B] = 0, then they share a common set of eigenvectors. To…

Q: Let Ra Cáãnt có ý) y tế + an Find VTRI b- Find √x , where is the gradient operator with respect to…

A:

Q: 5. Consider the following wavefunctions. Determine which are eigenfunctions of each operator listed.…

A: We have to find the eigen function and eigen value for the given operators

Q: 6. Find the general form of the function that satisfies dR/dt = kR.

A: it is kind of small font but i am assuming it's written asdRdt=kRwell we need to integrate so,…

Q: (b) f(x) = Acos(ax),                     = d2/dx2, where A and a are constants (c) f(x) = Ae-ax,…

A: By using eigenvalue equation, where for a function ψ the eigenfunction of operator Q^ Q^ψ = λψwhere…

Q: For a Hermitian operator Â, ſy°(x)[Â¥(x)]dx = [y(x)[Â¥(x)]*dx . Assume th ƒ(x)= (a +ib)f(x) where a…

A: The question asks us to show that , assuming  is hermitian operator. It's action on a function f(x)…

Q: An eigenvalue is a function that returns itself times a scalar when operated on by a linear operator…

A: Eigen value equation is given by

Q: b) Prove that the following operators are Hermitian 1) Z 2) Lx

A: (1) Z is z component of  position  operator. Since position operator r = (X, Y, Z) is hermitian.…

Q: Two wavefunctions, Y, and 42, are each eigenfunctions of the operator Ô, with eigenvalues wi and wz.…

A: Wavefunction The wavefunction of a particle is a mathematical function that encodes all the…

Q: (d) Consider the arbitrary ket |u)=i-1 uli), where i) is an orthonormal basis. i. Show that u =…

A:

Q: 2- find the matrix of two operators L, and L2 at l = 1 The given : (e",m'|L²|e, m) = l (l + 1)h²…

A: Given, l',m'L2l,m=ll+1h2δl,l'δm,m' So at l=1 l',m'L2l,m=2h2δl,l'δm,m' δl,l'δm,m'=1              for…

Q: Which function is an eigenfunction to the operator = k ax a.) f(x) = sin(ax) b.) c.) d.) e.) f(x)…

A: