# Tagged Questions

3answers
135 views

### Hilbert space of harmonic oscillator: Countable vs uncountable?

Hm, this just occurred to me while answering another question: If I write the Hamiltonian for a harmonic oscillator as $$H = \frac{p^2}{2m} + \frac{1}{2} m \omega^2 x^2$$ then wouldn't one set of ...
2answers
72 views

### Translator Operator

In Modern Quantum Mechanics by Sakurai, at page 46 while deriving commutator of translator operator with position operator, he uses $$\left| x+dx\right\rangle \simeq \left| x \right\rangle.$$ But for ...
4answers
266 views

### Is the momentum operator diagonal in position representation?

The matrix elements of the momentum operator in position representation are: $$\langle x | \hat{p} | x' \rangle = -i \hbar \frac{\partial \delta(x-x')}{\partial x}$$ Does this imply that \$\langle x ...
1answer
115 views

### Schrodinger equation in term of Fokker-Planck equation

From Wikipedia on the Fokker-Planck equation: \tag{1}\frac{\partial }{\partial t}f\left( x^{\prime },t\right) ~=~\int_{-\infty}^\infty dx\left( \left[ D_{1}\left( x,t\right) \frac{\partial ...
3answers
450 views

### Matrix elements of momentum operator in position representation

I have two related questions on the representation of the momentum operator in the position basis. The action of the momentum operator on a wave function is to derive it: \hat{p} ...
3answers
683 views

### Don't understand the integral over the square of the Dirac delta function

In Griffiths' Introduction to Quantum Mechanics he gives the eigenfunctions of the Hermitian operator $\hat{x}=x$ as being $$g_{\lambda}\left(x\right)~=~B_{\lambda}\delta\left(x-\lambda\right).$$ ...
1answer
164 views

### State normalization in Dirac's formulation of quantum mechanics

Let us divide the time $T$ into $N$ segments each lasting $δt = T/N$. Then we write $\langle q_F | e^{−iHT} |q_I \rangle = \langle q_F | e^{−iHδt} e^{−iHδt} . . . e^{−iHδt} |q_I \rangle$ Our ...
2answers
219 views

### Is the braket notation of the Dirac delta function symmetric?

I have a book saying, $\int \delta(x-x')\psi(x)dx = \psi(x')$ where $\psi(x) = \langle x\lvert\psi\rangle$, so our definition of delta function would be $\langle x'\lvert x\rangle = \delta(x-x')$. ...
1answer
78 views

### When does the “norm of quasi-eigenvectors” matter in calculations? For which physical results are these even used?

Which physical system in nonrelativistic quantum mechanics is actually described by a model, where the norm of the "position eigenstate" (i.e. the delta distribution as limit of vectors in the ...
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