Law of Conservation

Momentum is only coserved if there is no external force acting on the system. Now, in your example, YOUR BODY is the system. When you try to move fromrest, you need to exert a foce onto the ground by your legs. The reaction force acting on you, which pushes you forward, is given by the ground. As such, you are acted by an external force that leads to a change of momentum of your body.

Imagine that if you are walking on a very slippery road, or if you hang yourself in mid air, you won't be able to move forward even you move your legs. There is no external force acting on you. Your momentum doesn't change.

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"Quantum" implies "discrete". Unlike objects in the macroscopic world, which can have any arbitrary value of energy (say, potential or kinetic energy), particles in the microscopic world can only allow to have "discrete energies". This is similar to what happens in a high rise building. Persons who stay in the building can stay at the 1st floor, 2nd floor, 3rd floor....etc, but cannot stay at the "mid way" between, say the 2nd and 3rd floor. Thus, we can say that persons occupying the building are "height quantized" . The heights of their occupation above ground are discrete numbers, i.e. 1st floor (say, 10 ft above ground), 2nd floor (20 ft above ground), or 3rd floor (30 ft above ground)...etc. They cannot be at a height of, say 25.6 ft above ground.

Further, if we want to locate a particluar person in a building, we could find him, say in Room 1 inside Flat A on the 2nd floor. Thiese three numbers, Room 1, Flat A, 2nd floor, gives us a means to "characterize" the position of that person.....(cont'd)



2010-04-12 21:49:47 補充：
(cont'd)....In qunatum mechanics, if we want to locate where an orbital electrons is,...

2010-04-12 21:56:36 補充：
sorry...I don't know whu I can't continue posting the rest, may be I send you a mail for the rest of the answe.

When you try to move, you are adding additional force/energy/momentum to the system, it is not violationg the law.

quantum state are model that, created out of thin air, use by the clever people to try to confuse the normal people. It make big assumption and "IF" and only if the assumption is true, the theroy is correct. Normal People should not find it understanfable!

Moving does not violate momentum conservation if the object moves in uniform velocity.

A quantum state is a vector in some complex vector space (technically known as Hilbert space) with a dot product (eats two vectors and spits out a complex number).

e.g.
1. A quantum spin state of an electron is a vector in the two complex dimension vector space C^2 with a basis: spin up and spin down.

2. A spinless particle state is a complex-valued wave function in real space. The Hilbert space is the function space of square integrable functions L_2.

Expectation valued:
Physical observable quantities are represented as a linear operator (eats a vector and spits out another vector).

e.g. (Set hbar = 1)
1. Quantum spin: S_z = (1/2) diagonal matrix( 1 , -1 )

2. Momentum = - i d/dx, where i = Sqrt(-1) and d/dx = differentiation w.r.t. x

Expectation value of a physical observable A of a given state v is given by the dot product between v and Av:
average(A) = v . Av
if v is normalized, i.e. v.v = 1.