Recent content by Nixom

Do you mean CM can be formulated in the same formalism with QM? So the difference is due to the definition of products. Do I get it?

Thanks for the advice, maybe I should get a copy first. Could you give me a brief abstract about the author's viewpoint?

Actually the appearance of the concept of QM state is also indigested to me, it shows up in an "unusal" way in the QM axiom as a new concept. In my opnion, the state of CM defined in phase space by (x,p) is not a comparable thing even in mathematical sense. Is is necessary to create such entity...

In textbooks, the analog between Poisson bracket and commutator is considered as the bridge connecting CM and QM formalism, converting Poisson bracket into commutator is always the common procedure for quantization. After the convert, the energy of harmonic oscillator system become quantized due...

In many textbooks, the non-commutativity for the canonical pair is considered to lead to the major variaty from classical mechanism(CM) to quantum mechanism(QM), and change the Possion bracket into quantum commutator is a standard procedure called as canonical quantization. But in fact the...

thanks, Sam. It seems that the most important property of physical quantities is that they are conserved, is it? And why the conserved quantities just happen to have those properties, is there some mechanism guaranteeing this? By the way, which algebra dose the commutator [x,p] or the...

Sorry for the obscure question. I just wonder why we can identify the generators of Lorentz group as the physical variables, such as placement for momentum, rotation for angular momentum... Is it because they have the same algebra relation as the classical Possion brackets?

Can someone tell me why the quantities having the same algebra structure can be indentified as the same dynamical variables? Are the Possion brackets and the quantum commutators two different presentation of the same Lie algebra?

In most of textbooks, the canonical quantization procedure is used to quantize the hamiltonian with a simple form, the quadratic form. I just wonder how should we deal with more complex form hamiltonian, such like the ones including interaction terms?

I have some questions about the matrix <0|j^{\mu}_5|\pi(p)>=if_{\pi}p^{\mu} 1.Pi is a psuedoscalar particle, but the current between vacuum and pi state is an axial one, why not a psuedoscalar one? And how do we determine the current appearing in the similar matrix like <0|j|meson>...

If I expand x\propto(a+a^\dagger) in the Hamiltonian H=\frac{p^2}{2m}+\frac{1}{2}m\omega^2x^2+\lambda x^4, I can't get the results such as [H,a^\dagger]=\omega a^\dagger or [H,a]=-\omega a, so how can I interpret them as creation and annihilation operators? The commutation relations of these...

OK,if I originally take the a+ and a- as the Fourier coefficients, can they be interpreted as creation and annihilation operators definitely, or it is just depend on some specific form in Hamiltonion, e.g. the quadratic form?

thanks, all guys

In the free case,we decomposite the free Hamiltonian into the creation and annihilation operators, i just wonder why this ad hoc method can not be used to the interaction theory?

i just wonder why we call it "sum rule"? waht do we sum, and what sum for?