Question

Which of the following phanomia can not be explained by classical machanics

Answer 1

• Classical mechanics was unable to explain certain phenomena: black body radiation, the photoelectric effect, the stability of atoms and molecules as well as their spectra. Quantum mechanics, created mainly by Werner Heisenberg and Erwin Schrödinger, explained these effects.

Answer 2

m Answer:

Classical mechanics was unable to explain certain phenomena: black body radiation, the photoelectric effect, the stability of atoms and molecules as well as their spectra. Quantum mechanics, created mainly by Werner Heisenberg and Erwin Schrödinger, explained these effects.

Explanation:

 

The function

is called the Lagrangian function and the action can be written as

The quantity  is called kinetic energy and motions satisfying [1] conserve energy as time t varies, that is,

[3]

Hence the action principle can be intuitively thought of as saying that motions proceed by keeping constant the energy, sum of the kinetic and potential energies, while trying to share as evenly as possible their (average over time) contribution to the energy.

In the special case in which V is translation invariant, motions conserve linear momentum  if V is rotation invariant around the origin O, motions conserve angular momentum , where ∧ denotes the vector product in , that is, it is the tensor (a ∧ b)ij = aibj−biaj, i, j = 1,…,d: if the dimension d = 3 the a ∧ b will be naturally regarded as a vector. More generally, to any continuous symmetry group of the Lagrangian correspond conserved quantities: this is formalized in the Noether theorem.

It is convenient to think that the scalar product in  is defined in terms of the ordinary scalar product in , by : so that kinetic energy and line element ds can be written as  and , respectively. Therefore, the metric generated by the latter scalar product can be called kinetic energy metric.

The interest of the kinetic metric appears from the Maupertuis' principle (equivalent to [1]): the principle allows us to identify the trajectory traced in  by a motion that leads from X1 to X2 moving with energy E. Parametrizing such trajectories as τ → X(τ) by a parameter τ varying in [0, 1] so that the line element is ds2 = (∂τX, ∂τX) dτ2, the principle states that the trajectory of a motion with energy E which leads from X1 to X2 makes stationary, among the analytic curves , the function

[4]

so that the possible trajectories traced by the solutions of [1] in  and with energy E can be identified with the geodesics of the metric .

For more details, the reader is referred to Landau and Lifshitz (1976) and Gallavotti (1983).

Introduction to Quantum Mechanics

Yehuda B. Band, Yshai Avishai, in Quantum Mechanics with Applications to Nanotechnology and Information Science, 2013

assical mechanics point of view. This situation of discrete energies exists not only for hydrogen atoms, but for all atoms and molecules, and in fact for all bound states of quantum systems. This said, we further note that a continuum of energies is possible for unbound states (in thAs an aside, we note that sometimes the frequency of a photon is given as the angular frequency ω in units of radians per secon1, , and bound states exist for every integer value of n (we shall consider the hydrogen atom in detail in Sec. 3.2.6 – here, simply note that bound states of a hydrogen atom exist only at very special values of energy).

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