States, atomic stationary

The atom has only specific, allowable energy levels, called stationary states. Each stationary state corresponds to the atom s electrons occupying fixed, circular orbits around the nucleus. 

While in one of its stationary states, atoms do not emit energy. 

Ket notation is sometimes used for functions in quantum mechanics. In this notation, the function / is denoted by the symbol j/) /—1/>. Ket notation is convenient for denoting eigenfunctions by listing their eigenvalues. Thus nlm) denotes the hydrogen-atom stationary-state wave function with quantum numbers , /, and m. 

Fig. 9.9. Contour plot of the potential energy surface of H2O in the AlB state the bending angle is fixed at 104°. Superimposed are the total stationary wavefunctions I tot( ) defined in (2.70). The total energies are —2.6 eV and -2.0 eV corresponding to wavelengths of A = 180 nm and 165 nm, respectively. Energy normalization is such that E = 0 corresponds to three ground-state atoms.

It was emphasized in Chapter 6 that the definition of an atomic stationary state property is determined by the form of the atomic stationary state functional fl]. In precisely the same manner, the definition of an atomic property in the general time-dependent case is determined by the form of the atomic Lagrangian integral 2,t]. In both the stationary-state and... 

Calculate the uncertainty AL for these hydrogen-atom stationary states (a) 2p/,... 

A closed atomic system is capable of existing in a series of states, the stationary states, having energy values which in general form a discrete sequence and possessing a peculiar stabihty such that any change of energy of the system consists in a transition from one stationary state to another. 

In our first experiments on the kinematic cooling process, we chose to scatter a molecular beam of NO from an atomic beam of argon. The energetics were selected to provide a velocity vector cancellation that results in the the post collision NO7 5 (NO in the j = 7.5 rotational state) being stationary in the laboratory frame. We will show below why this quantum state of NO is essentially stationary in the laboratory reference frame,... 

Applications of quantum mechanics to chemistry invariably deal with systems (atoms and molecules) that contain more than one particle. Apart from the hydrogen atom, the stationary-state energies caimot be calculated exactly, and compromises must be made in order to estimate them. Perhaps the most useful and widely used approximation in chemistry is the independent-particle approximation, which can take several fomis. Conuiion to all of these is the assumption that the Hamiltonian operator for a system consisting of n particles is approximated by tlie sum... 

All the previous discussion in this chapter has been concerned with absorption or emission of a single photon. However, it is possible for an atom or molecule to absorb two or more photons simultaneously from a light beam to produce an excited state whose energy is the sum of the energies of the photons absorbed. This can happen even when there is no intemrediate stationary state of the system at the energy of one of the photons. The possibility was first demonstrated theoretically by Maria Goppert-Mayer in 1931 [29], but experimental observations had to await the development of the laser. Multiphoton spectroscopy is now a iisefiil technique [30, 31]. 

The forces in a protein molecule are modeled by the gradient of the potential energy V(s, x) in dependence on a vector s encoding the amino acid sequence of the molecule and a vector x containing the Cartesian coordinates of all essential atoms of a molecule. In an equilibrium state x, the forces (s, x) vanish, so x is stationary and for stability reasons we must have a local minimizer. The most stable equilibrium state of a molecule is usually the... 

In Figure 2.2(a) states m and n of an atom or molecule are stationary states, so-called because they are time-independent. This pair of states may be, for example, electronic, vibrational or rotational. We consider the three processes that may occur when such a... 

Atomic and Molecular Energy Levels. Absorption and emission of electromagnetic radiation can occur by any of several mechanisms. Those important in spectroscopy are resonant interactions in which the photon energy matches the energy difference between discrete stationary energy states (eigenstates) of an atomic or molecular system = hv. This is known as the Bohr frequency condition. Transitions between... 

The modern theory of the behavior Of matter, called quantum mechanics, was developed by several workers in the years 1925-1927. For our purposes the most important result of the quantum mechanical theory is that the motion of an electron is described by the quantum numbers and orbitals. Quantum numbers are integers that identify the stationary states of an atom the word orbital means a spatial description of the motion of an electron corresponding to a particular stationary state. 

All atoms have stationary states and can hold only particular values of energy. 

According to this scheme an atom of sulphur, for example, with sixteen electrons, would have an electronic configuration of 2, 4, 4, 6 (Bohr [1923]). The main feature of the building-up procedure was Bohr s assumption that the stationary states would also exist in the next atom, obtained by the addition of a further electron. He also assumed that the number of stationary states would remain unchanged apart from any additional states of the newly introduced electron. In other words the assumption was one of the existence of sharp stationary states, and their retention on adding both an electron and a proton to an atom. To quote Bohr ... 

It should be added that the stationary states in the newly obtained atom are not identical, since the accompanying addition of a proton causes a contraction in the size of the electron orbits. 

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