BioPHYSICAL chemistry
Using this expression for velocity from eqn 9.17 gives us the wavelength as: =6.1 × 10 −^12 m (9.22) The ability to manipulate t ...
with a factor of iZ. Since the wavefunctions usually involve more than one dimension, for example, x, y, and zfor a three-dimens ...
x=rsinθcosφ y=rsinθsinφ (9.29) z=rcosθ To make use of these two coordinate systems in Schrödinger’s equation it is necessary to ...
ψ(r,t) =ψ(r)e−iωt=ψ(r)e−iEt/Z as ω=E/Z (9.34) With this substitution we can write: (9.35) Using the relationship that: (9.36) gi ...
so equivalently: ψ(x) =Aeikx (9.42) Substitution into eqn 9.39 gives: (9.43) (9.44) (9.45) (9.46) Born interpretation The physic ...
2 The wavefunction may be a complex function but the probability is always real, since: ψ(x) =A(x) +iB(x) ψ*(x) =A(x) −iB(x) (9. ...
and no sharp turns are allowed; that is, the wavefunction must be smooth and continuous. 6 The solution to Schrödinger’s equatio ...
variables for distance. We also will need to determine the number of degrees of freedom, whether the object is constrained to mo ...
momentum, and energy. Thus, the classical ideal of precise determination of the properties of objects gave way to an interpretat ...
A quantum-mechanical world Under common circumstances, people do not encounter effects such as the wavelength nature of matter o ...
Research direction: Schrödinger’s cat The unusual features of quantum theory resulted in heated debate about the correctness of ...
Superconductors play a critical role in many instruments, including mag- nets used for NMR experiments (Chapter 14). In a SQUID, ...
Problems 9.1 Calculate the velocity of an electron if it has a wavelength of (a) 2.0 Å, (b) 1.0 Å, and (c) 10.0 Å. 9.2 Calculate ...
9.20 What is the uncertainty in position of a proton that has an uncertainty in velocity of (a) 10 Å s−^1 , (b) 1 Å s−^1 , and ( ...
An understanding of the properties of biological molecules requires know- ledge of quantum mechanics. This chapter presents two ...
the solution to use is based upon experience in solving differential equa- tions. For this situation, consider the general solut ...
We now have determined the parameters Band k, and have the follow- ing solutions: (10.9) (10.10) To determine the last parameter ...
(Figure 10.2). The wavefunctions are related to each other by n, with the different solutions corresponding to harmonics of the ...
state is also symmetrical but with the wave- function having a change in sign, correspond- ing to negative parity. The change in ...
(10.21) This term equals 1 when l =L, 0.5 when l =L/2, and 0.05 when l =0.2L. Orthogonality One of the special properties of eig ...
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