bei48482_FM
thereby opening wide the door to the modern view of the atom which others had only pushed ajar. By June Schrödinger had applied ...
168 Chapter Five instance, in the case of the electron in a hydrogen atom, only the electric field of the nucleus must be taken ...
Figure 5.2(a) Arrangement of double-slit experiment. (b) The electron intensity at the screen with only slit 1 open. (c) The ele ...
mechanics wave functions add, notprobabilities. Instead the result with both slits open is as shown in Fig. 5.2e, the same patte ...
position of the single particle is (5.18) If is a normalized wave function, the denominator of Eq. (5.18) equals the prob- abil ...
5.6 OPERATORS Another way to find expectation values A hint as to the proper way to evaluate p and E comes from differentiating ...
and so we have KˆE 2 (5.26) Equation (5.25) therefore reads iU (5.27) Now we multiply the identity by Eq. (5.27) ...
Every observable quantity Gcharacteristic of a physical system may be represented by a suitable quantum-mechanical operator Gˆ. ...
A familiar and quite close analogy to the manner in which energy quantization occurs in solutions of Schrödinger’s equation is w ...
experiments performed on hydrogen atoms always show that each one contains a whole electron, not 27 percent of an electron in a ...
so we can say that the various Enare the eigenvalues of the Hamiltonian operator Hˆ. This kind of association between eigenvalue ...
since U0 there. (The total derivative d^2 dx^2 is the same as the partial derivative ^2 x^2 because is a function only of x ...
of (^) n^2 over all space is finite, as we can see by integrating (^) n^2 dxfrom x0 to xL (since the particle is confine ...
Example 5.4 Find the probability that a particle trapped in a box Lwide can be found between 0.45Land 0.55Lfor the ground and fi ...
Quantum Mechanics 181 Example 5.5 Find the expectation value x of the position of a particle trapped in a box Lwide. Solution Fr ...
With anLwe have p sin^2 L 0 0 since sin^20 sin^2 n 0 n1, 2, 3,... The expectation value p of the particle’s momentu ...
Quantum Mechanics 183 Hence each energy eigenfunction can be expressed as a linear combination of the two wave functions (^) n ...
which we can rewrite in the more convenient form a^2 0 (5.53) where a (5.54) The solutions to Eq. (5.53) are real exponentia ...
Quantum Mechanics 185 necessarily great, but not zero either—of passing through the barrier and emerging on the other side. The ...
Example 5.6 Electrons with energies of 1.0 eV and 2.0 eV are incident on a barrier 10.0 eV high and 0.50 nm wide. (a) Find their ...
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