In classic mechanic,if we regard ##v_i## as a field ##v_i(t,x_1,x_2,x_3,x_4)##,
the poisson braket ##(v_i,x_i)=\frac{\partial{v_i}}{\partial{p_i}}=\frac{\partial{v_i}}{\partial{x_i}}\frac{\partial{x_i}}{\partial{p_i}}+\frac{\partial{v_i}}{\partial{t}}\frac{\partial{t}}{\partial{p_i}}=0##,
so...
##\hat{v}_i=c\hat{\alpha}_i## commute with ##\hat{x}_i##,
##E^2={p_1}^2c^2+{p_2}^2c^2+{p_3}^2c^2+m^2c^4##
But in classical picture,the poisson braket...
Thanks.I think Bohmian mechanics is helpful to me.Could help me with another question below?
##\psi## is a solution of Schrodinger eqution.
When ##\hbar \rightarrow 0##,##{\psi}(x,t) \rightarrow {\rho}(x,t)e^{\frac{i}{\hbar}S(x,t)}##
Define...
Thanks.
How about this way.
Classic Mechanic :
1,wave function (##\hbar \rightarrow 0##) is ##\psi \rightarrow \exp{\frac{i}{\hbar}S(x,t)}##;
2,we get wave function from Hamilton-Jaccobi equation with boundary condition...
The classic limit of Schrodinger equation is hamilton-jacobi eqution.
Wave function's classic limit is ##\exp{\frac{i}{\hbar}S(x,t)}##,##S(x,t)## is the action satisfying hamilton-jaccobi eqution.
However, a particle travels along single trajectory of ##S(x,t)##,
Why not make some constrains...
Thanks!
I means with the perturbation added, the atom in ##{\phi}_n## with time evolving to be fould in ##\Psi=\sum\limits_{m=0}^{\infty}a_m(t){\phi}_m\exp{(-\frac{i}{\hbar}{E_m}t)}##,this is a mixture of many eigenstates.However,as the book said,the atom would be found at another eigenstate in...
Thanks.I check my book and I am mistaken.But I am still confused.
As the book said,
##{\phi}_n## is the eigenstate of time-independent schrodinger equation with eigenvalue ##E_n##.
Adding the time-dependent perturbation ##{\hat{H}}^{'}(t)##, wave function becomes...
The radiation of an atom was interpreted by time-independent schrodinger equation:electron was transformed from high energy level state to lower and emit a photon.Could we treat this process through a wavefunction ##{\psi}(t)##? Before emiting,the system's wavefunction is ##{\psi}(0)## and after...
Homework Statement
I have some doubts about the method constructing chemical reaction process of quantum mechanics in the referencehttp://www.southampton.ac.uk/assets/centresresearch/documents/compchem/DFT_L2.pdf, for the example of ##H_2O## molecular dissociation to ##H^+## and ##OH^-## ions...
Homework Statement
The fresnel-kirchhoff diffraction formula could explain diffraction,I think it should also produce the result with relatively small wavelength and large width slit in which case there is no diffraction.
Homework Equations...
Thanks very much.I still want to get deeper.I think two ways to understand the double-slit electron diffraction only to get both stuck.
1,Solving Schordinger equation to get the wavefunction:boundary condition is necessary.But I have no ideas to set a boundary condition.
2,Regard slit as point...
Thanks very much!It seems that there is more precise interpretation for electron diffraction.Could you tell me?
Nice.I try to figure out the ##A(x,t)##,failed with there consideration,because whether or not measure the limited angle of electrons confuse me:
1,if an electron's path could not be...
I exactly missed something.The wave function ##{\phi}(x,t)=Ae^{\frac{i}{\hbar}S(x,t)}## spread over all space-time,it has value at arbitrary (x,t).Some improvements needed...I think...
Homework Statement
I post here to check if I am in the right way to understand this point in the book.
The wave function of free particle is ##Ae^{\frac{i}{\hbar}(px-Et)}##.This could be regarded as ##{\phi}(x,t)=Ae^{\frac{i}{\hbar}S(x,t)}##.
##S(x,t)## is the free particle's least action...
<Moved from the homework section>
1. Homework Statement
I have read several chapters of De Brogile's article "the theory of quanta".The motion of a particle could be analogious to a ray in general optics.This is an analogy between Maupertui's principle and fermat's principle.
How to use this...