Tagged Questions
-2
votes
0answers
30 views
Why is the expectation value of the Hamiltonian/position commutator equal to zero?
I know that the commutator $[H,x]$ is $-i \hbar \,p/m$, but how do I show that the modulus of the expectation value of this is zero?
5
votes
4answers
288 views
Does uncertainty imply noncommutativity?
We already know that non-commutativity of observables leads to uncertainty in quantum mechanics cf. e.g. this and this Phys.SE post. What about the opposite: Does uncertainty imply noncommutativity?
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4
votes
3answers
1k views
Proof of Canonical Commutation Relation (CCR)
I am not sure how $QP-PQ =i\hbar$ where $P$ represent momentum and $Q$ represent position. $Q$ and $P$ are matrices. The question would be, how can $Q$ and $P$ be formulated as a matrix? Also, what is ...
3
votes
2answers
161 views
Why does $i ( LK-KL )$ represent a real quantity?
According to my textbook, it says that $i( LK-KL )$ represents a real quantity when $K$ and $L$ represent a real quantity. $K$ and $L$ are matrices. It says that this is because of basic rules. ...
4
votes
3answers
348 views
Generalizing Heisenberg Uncertainty Priniciple
Writing the relationship between canonical momenta $\pi _i$ and canonical coordinates $x_i$
$$\pi _i =\text{ }\frac{\partial \mathcal{L}}{\partial \left(\frac{\partial x_i}{\partial t}\right)}$$
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