# Tag Info

Accepted

### How can Planck's constant take different values?

In a purely classical (Newtonian) universe, quantum effects would be absent, and the way to pretend this is true mathematically is to allow Planck's constant to approach zero, and see what the ...
• 92.1k
Accepted

### On Groenewold's Theorem and Classical and Quantum Hamiltonians

You probably need to internalize Ivan Todorov's accessible Quantization is a mystery. Your best bet for addressing your questions is Geometric quantization, not phase space quantization that you ...
• 61.8k

### Is Planck's Constant Really a Constant?

How did he assume that $\frac{\hbar}{i}=1$? He didn't. Check the definition he gives of the commutator in equation (1.02). And if $\hbar$ (as we have learned it) is a constant how can we say that ...
• 900

• 1,184

### A Hamiltonian with a potential depending on the momentum

You have an embarrassment of riches, and you have to use symmetry or other physical information to restrict your choice! This is dubbed the "operator ordering ambiguity problem", and has ...
• 61.8k

### How can Planck's constant take different values?

From a mathematical perspective, it is interesting to study quantum theories, where the (reduced) Planck's constant is not necessarily equal to its physical value. For instance, In the mathematical ...
• 200k

### Physical interpretation of differences between classical and quantum ensemble dynamics

Cosmas Zachos has already given a nice answer. He correctly points out that the sine function in the $\star$-commutator originates from the exponential function in the $\star$-product. Question: ...
• 200k

### Heisenberg group deformation

I'm not sure I am understanding the quest, but, in plain phase space (q,p) with the standard Groenewold(-Moyal) star product, and arbitrary deformation parameter, here taken to be i, your construct is ...
• 61.8k

### Quantum systems without a classical analogue?

1) It is true that not all quantum systems have classical analogues. E.g. if we have a quantum algebra $({\cal A},\ast)$ of Laurent polynomials in an indeterminate $\hbar$, and endowed with an ...
• 200k

### Angular Momentum Addition in Phase Space QM

I could give you an answer by barking up a very different tree indeed! In phase space QM, and not, repeat not geometric quantization, you may work on flat phase spaces and forfeit spheres altogether, ...
• 61.8k

### Weyl Ordering Rule

Another way to look at this: $e^{ix\hat{P}+ik\hat{Q}}$ is automatically Weyl-ordered. This is because each term in the Taylor expansion, $\frac{1}{n!}(ix\hat{P}+ik\hat{Q})^n$, is Weyl-ordered. You can ...
• 3,864
Accepted

### Classical limit in deformation quantization

It might be worth reviewing formulas such as (122,34,5; 131) of our book, but, frankly, I am not sure I understand what underlies and follows the question, and especially the classical limit ...
• 61.8k