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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 6.055J / 2.038J The Art of Approximation in Science and Engineering Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . 6.055 / Art of approximation 56 The other possibility is to add quantum mechanics, which was developed to solve funda mental problems like the existence of matter. The physics of quantum mechanics is com plicated, but its effect on dimensional analyses is simple: It contributes a new constant of nature ~ whose dimensions are those of angular momentum. Angular momentum is mvr , so [ ~ ] = ML 2 T − 1 . The ~ might save the day. There are now two quantities Var Dim What containing time dimensions. Since e 2 / 4 π 0 has T − 2 and a 0 L size ~ has T − 1 , the ratio ~ 2 / ( e 2 / 4 π ) contains no time dimen e 2 / 4 π 0 ML 3 T − 2 sions. Since m e M electron mass " ~ 2 # ~ ML 2 T − 1 quantum = ML , e 2 / 4 π 0 a dimensionless group is ~ 2 a m e ( e 2 / 4 π ) It turns out that all dimensionless groups can be formed from this group. So, as in the It turns out that all dimensionless groups can be formed from this group....
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This note was uploaded on 02/24/2012 for the course MECHANICAL 6.055J taught by Professor Sanjoymahajan during the Spring '08 term at MIT.
 Spring '08
 SanjoyMahajan

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