2.2(The Results and Discussion of Solution of The Schrdinger Equation for A Single-electron atom) :

1 .2 3 4

1 2 3

1 2 3 CAI4 5

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: 1.HSchrdinger2.Schrdinger(1)Schrdinger(2)

() () R (r) : n=1,2,3,,n; l=0,1,2,,n-1; m=0,1,2,,l 3.

(The physical significance of quantum numbers)1n(The principal quantum number, n.) 1n The principal quantum number n determines the energy level of a hydrogenlike atom.n=1,2,3,. 2S2P1s 3S3P1s

n(The principal quantum number, n.)2The numbers degenerate eigenstate

nlm n23:n-1

The zero-point effectquantum effectE1s=-13.6eV.: (Virial Theorem) :

13.6eV,

1.The physical significance of quantum numbers The not only determines the distribution of the probability density of the election in space but also determines the properties of the microscopic system in that state. In discussing the physical significance of quantum numbers, the relationships between the properties of atoms and the wavefunction as well as the state of the electron spin are explained.

1). The principal quantum number, n.1n The energy operator is applied to the wave function which is the Schrdinger equation. Each of then obtained from solving this equation being operated on by is equal to a constant En multiplied by n i. e. the energy state n has energy En. This is the restriction on En in the solution of the R-equation.

1). The principal quantum number, n. 1nThe formula for the energy states of a one-electron atom is n=1,2,3,.)

The principal quantum number n determines the energy level of the system. The zero-point effect is a quantum effect of a particle..

2l (Azimulthal quantum number l.)1 lThe Azimulthal quantum number l determines the angular momentum of the atomic orbitals of the electron

2l (Azimulthal quantum number l.)2l the magnetic moment Bohr magneton-e/2mec-magnetogytric ratio

2. Azimulthal quantum number l. 2lthe absolute value of the angular momentum has definite values. This quantum number determines the angular momentum of the atomic orbitals of the electron hence the name azimuthal quantum number. The angular

momentum and the magnetic moment of an atom are related.

2. Azimulthal quantum number l. 2l-e/2mec is the ratio of the orbital magnetic moment to the orbital angular momentum, also known as the magnetogytric ratio of oribital motion. Hence the magnetic moment || is related to the quantum number l for an electron by B is the Bohr magneton, a unit of magnetic moment.

3. m (Magnetic quantum number m.)1zMzm determines the z-component of the angular momentumm=012, l

3. m (Magnetic quantum number m.)2z.m determines the component z of the magnetic moment in the direction of magnetic field.(3),,0, E = -z H = m B H

d

2l+1

3.Magnetic quantum number m.3. mThe operator of the z-component of the angular momentum. The z-direction is the direction of magnetic field. The physical significance of m is one which determines the z-component of the atom and also determines the component z of the magnetic moment in the direction of magnetic field.

3.Magnetic quantum number m.3. mm=012, l

ms 2s+1=2s=1/2 ms= , , 4.ss=1/2

n,l,m ms=1/2:, ms=-1/2:

(The wavefunction of a single-electron)1.

,n,l,mnlm,n,l,mnlmatomic orbital orbitorbitalatomic orbital

1) Rn,l(r)(The radial wavefunction)n-l-1n-l2. (Feature of wavefunction)

Yl,m( , )(The spherical harmonics wavefunction) l n-1 3) n

2pz

2Two types of wavefunction(Real wavefunction and complex wavefunction) n,l,m 100 2112px, 2pyx,y,z

2pxm=1 2pym=-1 2px2py211211 1 eigenstate)

EMMZ 210 211 31133

2Li2+1Li2+2Li2+2s2p

. . 19959CERN9. 410-8s 310-8s410-10s. .