Bra ket Definition and 22 Threads

The wavefunction of ##|\psi\rangle## is given by the bra ket ##\psi (x,y,z)= \langle r| \psi\rangle## I can convert the wavefunction from Cartesian to polar and have the wavefunction as ## \psi (r,\theta,\phi)## What bra should act on the ket ##|\psi\rangle## to give me the wavefunction as ##...

"## \left[-\frac{\hbar^{2}}{2 m} \frac{\partial^{2}}{\partial x^{2}}+V(x)\right]\langle x \mid E\rangle=E\langle x \mid E\rangle## is often referred to as the time-independent Schrödinger equation in position space. This equation also results from projecting the energy eigenvalue equation...

I can't follow how the above argument leads to (1.8). I am able to prove it only if I can show ##\langle a \mid c\rangle\langle b+c\rangle=(\langle a|+\langle b|) c\rangle## but I don't understand why the bra transformations <P| ,<Q| obey (<P|+ <Q|)x = <P|x + <Q|x . Is it an assumption...

We denote a scalar product of two vectors ##a, b## in Hilbert space ##H## as $(a,b)$. In Bra Ket notation, we denote a vector a in Hilbert space as ##|a\rangle##. Also we say that bras belong to the dual space ##H##∗ . So Bras are linear transformations that map kets to a number. Then it...

It's easy to show that ##[\Delta A, \Delta B] = [A,B]##. I'm specifically having issues with evaluating the bra-ket on the RHS of the uncertainty relation: ##\langle \alpha |[A,B]|\alpha\rangle = \langle \alpha |\Delta A \Delta B - \Delta B \Delta A|\alpha\rangle## The answer is supposed to be...

Homework Statement Let ##\vec{e}\in\mathbb{R}^3## be any unit vector. A spin ##1/2## particle is in state ##|\chi \rangle## for which $$\langle\vec{\sigma}\rangle =\vec{e},$$ where ##\vec{\sigma}## are the Pauli-Matrices. Find the state ##|\chi\rangle## Homework Equations :[/B] are all given...

Homework Statement Homework Equations I'm not sure The Attempt at a Solution Here is the solution that I don't understand.

Homework Statement If I had two vectors say ⟨em|f⟩⟨f|em⟩ does this equal |⟨em|f⟩|2? e is a basis and f is some arbitrary function. I ask this because I have a problem which is to show the following: Show that for the Fourier expansion of |f⟩ in terms of Fourier basis vectors |em⟩ is...

Question Consider the matrix $$ \left[ \matrix { 0&0&-1+i \\ 0&3&0 \\ -1-i&0&0 } \right] $$ (a) Find the eigenvalues and normalized eigenvectors of A. Denote the eigenvectors of A by |a1>, |a2>, |a3>. Any degenerate eigenvalues? (b) Show that the eigenvectors |a1>, |a2>, |a3> form an...

Dear All, I am trying to understand what operators actually mean when deriving the definition of green's function. Is this integral representation of an operator in the ##x-basis## correct ? ## D = <x|\int dx|D|x>## I am asking this because the identity operator for non-denumerable or...

Just checking (while trying to prove the Schwarz inequality for $<f|H|g>$, I know $ <f|g>=<g|f>^* $ please confirm/correct : If $ \psi=f+\lambda g, \:then\: \psi^*=f^*+\lambda^* g^* $ Is $ <f^*|g>=<g^*|f>^* $ and $ <f^*|H|g>=<g^*|H|f>^* $ (H hermitian)? Is $ <f^*|H|g><g^*|H|f> = -...

I am trying to understand the mathematics of quantum eraser experiments, in order to deepen my understanding of what is really happening. The paper I am currently working on is: "A double-slit quantum eraser" by S. P. Walborn, M. O. Terra Cunha, S. Padua, and C. H. Monken (2001) in which a...

Homework Statement Rewrite the state |ψ⟩ = √(1/2)(|0> + |1>) in the new basis. |3⟩ = √(1/3)|0⟩ + √(2/3)|1⟩ |4⟩ = √(2/3)|0⟩ − √(1/3)|1⟩ You may assume that |0⟩ and |1⟩ are orthonormal. Homework Equations The Attempt at a Solution [/B] I have a similar example in my notes however there...

Hello everyone, I have thi doubt: If I have a state, say psi1, associated with the energy eigenvalue E1, the integral over a certain region gives me the probability of finding the particle in that region with the specified energy E1. Now if I put an operator between the states I obtain its mean...

I'm trying to apply BRA KET notation to my notes on particle physics. please could someone confirm that the kroneker delta function may be written \delta _{ij} = \left \langle i |j \right \rangle OR would it be written δij = |i> <j| I know i and j are indices, so can BRA KET even be...

In class we went through the derivation of the energy of a perturbed system, I've dug my old notes out and found a bra ket derivation of the same thing, there's just one step that doesn't look right and was wondering if someone could tell me if its a misprint or actually correct (and why)...

say you have <ψ|x|ψ⟩ or <0|F|k⟩ where F is an operator, what does this actually mean? I understand C|ψ⟩ would be the operator C acting on PSI and <ψ1|ψ2⟩ is the inner product of two wavefunctions but what would a third term inbetween them mean? thanks for any help

The question is to calculate the time evoution of S_{x} wrt <\Psi(t)\pm l where <\Psi\pm (t) l= ( \frac{1}{\sqrt{2}}(exp(^{+iwt})< \uparrow l , \pm exp(^{-iwt})< \downarrow l ) [1] Sx=\frac{}{2}(^{0}_{1}^{1}_{0} ) Here is my attempt: - First of all from [1] I see that l \Psi\pm (t) > = (...

given: at t=0 |PSI(0)> = 1/2 |PSI1> + (SQRT3)/2 |PSI2> --------------------------------------------------------------------- my attempt so far: we can write |PSI1> = 1/2 |UP> + 1/2 |DOWN> |PSI2> = (SQRT3)/2 |UP> + (SQRT3)/2 |DOWN> therefore |PSI(0)> = 1/2 |UP> + 1/2...

1. Explain why <n|(a-a+)^3|n> must be zero 2. a and a+ (a dagger) are the raising and lowering operators (creation and annihilation operators). 3. Because it says explain, I am not sure any mathematical proof is needed. I am best answer is that because (ignoring that the bracket...

Looking for an online pdf refresher of bra ket algebra. Anyone have a recomendation?

Is the complex conjugate to the outer product this? : ( |a> <b| ) * = ( |b> <a| ) ?