Linked Questions
11 questions linked to/from Applying an operator to a wavefunction vs. a (ket) vector
5
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3
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857
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From bra & ket vectors to wave functions
I have a hard time understanding how the transition happens between the two. Starting from Schrödinger eqaution for kets:
$$i\hbar\frac{d}{dt}\left|\psi\left(t\right)\right\rangle =\hat{H}\left|\psi\...
- 1,048
5
votes
1
answer
792
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Expansion coefficients of an arbitrary state in the Hilbert space of one-particle states
I was going through my notes on the unitary irreducible representations of the Poincare group and the subsequent construction of one particle states and I stumbled across the following steps in the ...
- 609
2
votes
3
answers
1k
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Confusion with Dirac Notation
I'm trying to calculate uncertainty in momentum, and I know that
$$\langle\hat P^2\rangle=\int^{\infty}_{-\infty}\hat P^2|\Psi(x)|^2\,\text dx$$
But I'm confused by what that symbol means. Does it ...
- 43
6
votes
1
answer
1k
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Equivalent definitions of vectors
Equivalent definitions of vectors.
In maths a vector is an object that obeys some axioms of a vector space. But in physics a vector can be thought as an object which is invariant under rotations of ...
- 12.6k
0
votes
2
answers
2k
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Energy basis to the X basis
On Shankar page 217 when going from the operator representation to the differential representation he starts with
$$a|0\rangle = 0$$
And says that with a projection on the X basis we get
$$|0\...
- 301
3
votes
2
answers
411
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Differentiation of a ket vector with respect to a spatial dimension
Consider a state $|\psi\rangle$. While discussing the Schroedinger equation, we say $$\hat{H}|\Psi(t)\rangle=i\hbar\frac{\partial}{\partial t}|\Psi(t)\rangle$$
We also define the hamiltonian operator ...
- 57
0
votes
1
answer
426
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Equivalence of Schrödinger's representation of state and Dirac's notation
I am slightly confused regarding the equation $$\psi(x)=\langle x|\psi\rangle $$
Now, basically from my initial knowledge about Dirac's notation, I am able to see the expression $\langle x|\psi\rangle ...
- 143
1
vote
2
answers
310
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In Quantum Mechanics is it possible to apply time evolution operator to wavefunction?
If I consider a wavefunction that is the superposition of Hamiltonian eigenfunctions, for example like: $$\psi(x)=\frac{1}{\sqrt{2}}\psi_1(x)+\frac{1}{\sqrt{2}}\psi_2(x)$$ with $\hat{H}\psi_1(x)=E_1\...
- 35
2
votes
2
answers
800
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Operator in quantum mechanics
I'm really confused by the definition and uses of operators in quantum mechanics. Usually we say that the state of a system is described by some vector $\lvert\psi\rangle$ in a Hilbert space $H$, and ...
- 4,776
1
vote
1
answer
158
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Different mathematical methods in quantum mechanics?
My understanding is that in quantum mechanics the wavefunction may be expressed as a function or as a ket vector (composed of many orthogonal ket vectors). I'm not too sure about the further ...
- 11
1
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1
answer
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Proof that rotational symmetric potential operators are scalar operators
Defintion: A scalar operator B is an operator on a ket space that transforms under rotations \begin{equation}\left| \xi ' \right >=\exp{(\frac{i}{h} \mathbf{\phi \cdot J})}\left| \xi \right >\...
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