(c) in a unidimensional potential field U = ax 2 /2, where a is
a positive constant;
(d) along a round orbit in a central field, where the potential
energy of the particle is equal to U = —alr (a is a positive con-
stant).
6.46. Taking into account the motion of the nucleus of a hydrogen
atom, find the expressions for the electron's binding energy in the
ground state and for the Rydberg constant. How much (in per cent)
do the binding energy and the Rydberg constant, obtained without
taking into account the motion of the nucleus, differ from the more
accurate corresponding values of these quantities?
6.47. For atoms of light and heavy hydrogen (H and D) find the
difference
(a) between the binding energies of their electrons in the ground
state;
(b) between the wavelengths of first lines of the Lyman series.
6.48. Calculate the separation between the particles of a system
in the ground state, the corresponding binding energy, and the
wavelength of the first line of the Lyman series, if such a system is
(a) a mesonic hydrogen atom whose nucleus is a proton (in a meso-
nic atom an electron is replaced by a meson whose charge is the
same and mass is 207 that of an electron);
(b) a positronium consisting of an electron and a positron revolving
around their common centre of masses.
6.2. WAVE PROPERTIES 0 F PARTICLES.
SCHRISHINGER EQUATION- The de Broglie wavelength of a particle with momentum p:
2rch
=- Uncertainty principle:
Ax • Ap, ih. - Schrodinger time-dependent and time-independent equations:
2
ih hV2tif+UW'
2m
V 21 i) (E —U) CI,where is the total wave function, II) is its coordinate part, V 2 is the Laplace
operator, E and U are the total and potential energies of the particle. In spheric-
al coordinates:
v2 = 02 2 a^1 a^ (sin 0 oao 1 02 (6.2d)
Or 2 ' r ar 2 sin 0 00 r2 silo^ 0,:1,2 •(6.2a)(6.2b)(6.2c)