# acceptable wave function examples

This makes the wave function If it is, then the integral of the square modulus of the wavefunction is equal to infinity, and the normalisation constant is zero. It is certain to be found at the point where the wavefunction is infinite, but this is acceptable. 0000001279 00000 n Since ∫* If it is, then the integral of the square modulus of the wavefunction is equal to infinity, and the normalisation … The wave function is not continuous. 154 0 obj <> endobj 0000003803 00000 n 2.2 to 2.4. For a wave function to be acceptable over a specified interval, it must satisfy the following conditions: (i) The function must be single-valued, (ii) It is to be normalized (It must have a finite value), (iii) It must be continuous in the given The Born interpretation means that many wavefunctions which would be acceptable mathematical solutions of the Schrodinger equation are not acceptable because of their implications for the physical properties of the system. Comment(0) Chapter , Problem is solved. 154 27 <<8EC1A121A6B53A4796778066CF30719C>]>> Due to the multiple possible choices of representation basis, these Hilbert spaces are not unique. Since Chapter 40. quadratically integrable. hŞT‘ËN„0†÷c2!qĞ/tß)$‘ÒXÌÛÛ�2c\´Íw.íßÿ°²zªÌ° {w“®q�n0ÃyZ�F8a?ÚA/Ñ®Ge�ùæú8V¦›àpHØ‡OÎ‹;ÃMÓ�hàPĞb—°òEÙW5"0jü6g‹ ‰ÅööÔâl•F§L�pà\ğ"§´ 4íÿ|"xl;uú[¹äR.¥�E T‡æôqO”åDÇŒè>R¹Q¬,cånoy&Ês"ïÌ÷�¸ÜHQnÇ‰‚JOòX$^ì¦J\4FÍAdG’‚�´Üªc>ü2Làêš^�ó†Ò˜È¶`Ø`ğ:I;ÙàMXÉ¯ G¯‘Ä By comparison, an odd function is generated by reflecting the function about the y-axis and then about the x-axis. This is an acceptable wave function. Further, the requirement that the second derivative of the wavefunction should exist means that wavefunctions of this form are also not acceptable. moving in one dimension, so that its wave function (x) depends on only a single variable, the position x. The Born interpretation also renders unacceptable solutions of the Schrodinger equation for which |ψ|2 has more than one value at any point. This means that the integral ∫ * d ψψ τ must exist. The second derivative of this wavefunction is discontinuous at the point indicated, where the gradient of the line changes by more than 180º. endstream endobj 165 0 obj <> endobj 166 0 obj <>stream It is clearly absurd to suggest that the particle can be definitely located at multiple positions, so a wavefunction such as this is deemed an unacceptable solution: The requirement that the square modulus of the wavefunction must be single-valued usually implies that the wavefunction itself must be single valued, and this is the requirement that we shall normally impose. This scanning tunneling microscope image of graphite shows the most This makes the wave function “smooth”. 0000002952 00000 n This is thus an unacceptable wavefunction. (Mathematically speaking, the area under such a curve at the point where it is infinite is given by an infinite height multiplied by an infinitely narrow width, the value of which may be finite.). Moreover, the fact that in between the two regions the wave-function is null, imposes, according to the quantum mechanics that the particle should disappear from one region and re … %PDF-1.4 %âãÏÓ Sin (x) unfortunately doesn’t. y, ∂ ∂ ∂ ∂ψ ψ. x). Wavefunctions and the Born Interpretation, Electronic Transitions and the d2 Configuration. 0000001538 00000 n The grey lines indicate the region where the wavefunction is multivalued. This means that the integral ∫ * d ψ ψ τ must exist. All its . Note that this does not rule out the possibility of a wavefunction rising to infinity at a single point. Specifically, each state is represented as an abstract vector in state space. All of the properties of the ﬁrst wavefunction hold here too, so this simply describes The wave function ψ. must be continuous. 0000004840 00000 n 0000001101 00000 n The wave function ψ must be continuous. This is the wavefunction of a particle that is precisely located at one definite point in space. Figure \(\PageIndex{7}\): Examples of even and y, ∂ ∂ ∂ ∂ψ ψ. x). 0000000016 00000 n 1. The Wave Function in Quantum Mechanics Kiyoung Kim Department of Physics, University of Utah, SLC, UT 84112 USA Abstract Through a new interpretation of Special Theory of Relativity and with a model given for physical space 3. 2. 0000006940 00000 n 0000015044 00000 n Consider x t, is an unnormalized wave function. Unfortunately, this implies that the particle described by such a wavefunction has a zero probability of being anywhere where the wavefunction is not infinite, but is certain to be found at all points where the wavefunction is infinite.

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