It must as well be continuous and its 1st and second derivatives must be continuous as well. K is called the Propagation constant of the wave associated with particle and it has dimensions reciprocal of length. the value of k from (1.67) to (1.63). Stay tuned with BYJU’S for more such interesting articles. Sign in|Recent Site Activity|Report Abuse|Print Page|Powered By Google Sites. Wave function and it’s physical significance. Broglie’s Hypothesis of matter-wave, and 3. The time-independent Schrodinger's wave equation in region II, where V = 0. where the constant K must have discrete values, implying that the total energy of the, particle can only have discrete values. Attractive interaction between the electron and nucleus B. If we change the value of rAB, an analogous value of E(rAB) can be got. It is consequently the simplest molecular system that can be encountered in nature. long questions & short questions for Physics on EduRev as well by searching above. The concept of wave function was introduced in the year 1925 with the help of the Schrodinger equation. well except during collision with walls from which it rebounds elastically. The simplest description of a covalent bond is a shared pair of electrons. For the above cases of one-dimensional infinite and finite potential wells which of the following is true? written as, Substituting The hydrogen molecule has 2 electrons (e1 and e2) and two nuclei (A and B). Then, choose the correct option. are discrete not continuous. We can, write the traveling-wave solution in the form, A free particle with a well-defined energy will also have a well-defined wavelength, The probability density function is Y(x, t)Y*(x, t) = AA*, which is a constant, independent of position. The concept of wave function was introduced in the year 1925 with the help of the Schrodinger equation. There is zero probability of finding the particle at, Probability density is zero at x = 0, a/2 , a. The potential energy (U) for the hydrogen molecule ion is, The first two terms in equation represent the electrostatic attraction between the nuclei and the electron while the last term represents the repulsion between the nuclei. The Schrodinger equation is the name of the basic non-relativistic wave equation used in one version of quantum mechanics to describe the behaviour of a particle in a field of force. (1.66) and (1.67) equation (1.65) becomes, the corresponding wave functions A particle cannot penetrate these infinite, potential barriers, so the probability of finding the particle in regions I and. In quantum physics, a wave function is a mathematical description of a quantum state of a particle as a function of momentum, time, position, and spin. The Schrodinger equation is linear partial differential equation that describes the evolution of a quantum state in a similar way to Newton’s laws (the second law in particular) in classical mechanics. Then, the time-independent, wave equation can he written from Equation (2.13) as, The solution to this differential equation can be written in the form, Recall that the time-dependent portion of the solution is, This wave function solution is a traveling wave, which means that a particle moving. Since an exact solution of it isn't probable. If E is finite, the wave function must be, = 0, in both regions I and III. We shall then attain the energy E' in terms of c1, c2, c3, that we can minimise. The variation theorem states that out of the E1', E2',,.... En', one will be the smallest and that if the true energy of the system is E, the lowest computed value of Ei' (i= 1,2,3,4,,,) isn't smaller than the true energy of the system. The correct answers are: The solutions of this case can be obtained by substituting x by in The normalization constant will be same as in the case of a box centered x = a/2 , The energy levels are. The approximate method known as the variation process is often employed. This wave equation is simple and it is possible to get an exact solution for it. All measurable information about the particle is available. In this situation, we utilize an estimated technique to get the solution to the Schrodinger equation. That is E'≥ Etrue. As it happens, two electrons may share an atomic orbital; we say that these electrons are paired. This result means that the energy of the particle, is quantized. The case of a symmetric one dimensional box, is similar to the box from x = 0 to a. Schrödinger time independent equation. Ψ=A sin Kx + B cos K x (4). The 2 hydrogen atoms are symbolized via A and B while the only electron is represented by e-. This contains 10 Multiple Choice Questions for Physics Application Of Schrodinger Wave Equation – MSQ (mcq) to study with solutions a complete question bank. The latter will be acceptable if finite and single valued. This approach, which doesn't explicitly model bonds as existing between two atoms, is somewhat less appealing to the intuition than the valence bond approach. This wave equation is simple and it is possible to get an exact solution for it. Therefore, according to uncertainty principle it is difficult to assign a position to the electron. Both the bond orbital and the electron pair now "belong" to both of the atoms. Normalized Spherical Harmonics 4. We conventionally label the wave function for a 3-dimensional object as ψ(x, y, z). The potential V(x) as a function of position for this problem is shown in, Figure 2.5. principle in that a precise momentum implies an undefined position. We can therefore compute E for this fixed value of rAB. We know that the wave function must be continuous at the boundaries of potential well at x=0 and x=L, i.e. [for E < V0], The correct answers are: for infinite case & for finite case for infinite case & for the finite case. Your email address will not be published. In essence, we want to obtain an approximation value for E' for that acceptable wave function exists. Since 2009, Tutorsglobe has proactively helped millions of students to get better grades in school, college or university and score well in competitive tests with live, one-on-one online tutoring. These examples will demonstrate the techniques used in the solution, of Schrodinger's differential equation and the results of these examples will, provide an indication of the electron behavior under these various potentials.
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