File
... system can be found. No. of states are equal to the dimension of Hilbert space, which can be finite/infinite. ...
... system can be found. No. of states are equal to the dimension of Hilbert space, which can be finite/infinite. ...
Document
... Time ordering places the operators occurring earlier in time on right of operator occurring later time. Creation operator occurring earlier in time will be placed to right of annihilation operators. This is opposite to normal ordering in which annihilation operators are placed to write of creation o ...
... Time ordering places the operators occurring earlier in time on right of operator occurring later time. Creation operator occurring earlier in time will be placed to right of annihilation operators. This is opposite to normal ordering in which annihilation operators are placed to write of creation o ...
4 Operators
... where c is a constant and f (x) and g(x) are functions. We’ll consider two examples first is the D̂ and the second is Â2 = ()2 . For the differential operator we see that (d/dx)[f (x) + g(x)] = (d/dx)f (x) + (d/dx)g(x) (d/dx)[cf (x)] = c(d/dx)f (x) ...
... where c is a constant and f (x) and g(x) are functions. We’ll consider two examples first is the D̂ and the second is Â2 = ()2 . For the differential operator we see that (d/dx)[f (x) + g(x)] = (d/dx)f (x) + (d/dx)g(x) (d/dx)[cf (x)] = c(d/dx)f (x) ...
3.2 Conserved Properties/Constants of Motion
... only the phase changes as a function of time. A successive measurement will find always the same Eigenvalue. The energy and the expectation value of the operator A are thus always measurable at the same time. The state of as system is defined completely if all expectation values of those operators a ...
... only the phase changes as a function of time. A successive measurement will find always the same Eigenvalue. The energy and the expectation value of the operator A are thus always measurable at the same time. The state of as system is defined completely if all expectation values of those operators a ...
LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
... 16. State and prove Ehernfest’s theorem 17. Solve the Schrodinger equation for a linear harmonic oscillator. Sketch the first two eigenfunctions of the system. 18. Determine the eigenvalue spectrum of angular momentum operators Jz and Jz 19. What are symmetric and antisymmetric wave functions? Show ...
... 16. State and prove Ehernfest’s theorem 17. Solve the Schrodinger equation for a linear harmonic oscillator. Sketch the first two eigenfunctions of the system. 18. Determine the eigenvalue spectrum of angular momentum operators Jz and Jz 19. What are symmetric and antisymmetric wave functions? Show ...
Homework Set 3
... Note: the proofs of a) and b) are quite simple, and are very similar to the proofs given in class for the case of Hermitian operators. Part c) is actually worked out in the text! It is important to note the final result, namely, that a unitary operator Û can always be written in the form ˆ Uˆ = e i ...
... Note: the proofs of a) and b) are quite simple, and are very similar to the proofs given in class for the case of Hermitian operators. Part c) is actually worked out in the text! It is important to note the final result, namely, that a unitary operator Û can always be written in the form ˆ Uˆ = e i ...
LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
... 2. Prove explicitly that the momentum operator is a self-adjoint operator. 3. Write down the ground state energy eigenfunction of a simple harmonic oscillator? Sketch its graph. 4. Define the parity operator by its effect on a wave function. What are its eigenvalues? 5. If A is any Hermitian operato ...
... 2. Prove explicitly that the momentum operator is a self-adjoint operator. 3. Write down the ground state energy eigenfunction of a simple harmonic oscillator? Sketch its graph. 4. Define the parity operator by its effect on a wave function. What are its eigenvalues? 5. If A is any Hermitian operato ...