{"appState":{"pageLoadApiCallsStatus":true},"articleState":{"article":{"headers":{"creationTime":"2016-03-26T14:04:17+00:00","modifiedTime":"2016-03-26T14:04:17+00:00","timestamp":"2022-02-24T16:50:51+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Science","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33756"},"slug":"science","categoryId":33756},{"name":"Quantum Physics","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33770"},"slug":"quantum-physics","categoryId":33770}],"title":"Finding the x, y, and z Equations for Three-Dimensional Free Particle Problems","strippedTitle":"finding the x, y, and z equations for three-dimensional free particle problems","slug":"finding-the-x-y-and-z-equations-for-three-dimensional-free-particle-problems","canonicalUrl":"","seo":{"metaDescription":"","noIndex":0,"noFollow":0},"content":"At some point, your quantum physics instructor may want you to find the x, y, and z equations for three-dimensional free particle problems. Take a look at the x equation for the free particle,\n<img src=\"https://www.dummies.com/wp-content/uploads/397870.image0.png\" width=\"140\" height=\"43\" alt=\"image0.png\"/>\nYou can write its general solution as\n<img src=\"https://www.dummies.com/wp-content/uploads/397871.image1.png\" width=\"456\" height=\"156\" alt=\"image1.png\"/>\nwhere Ay and Az are constants. \nBecause \n<img src=\"https://www.dummies.com/wp-content/uploads/397872.image2.png\" width=\"180\" height=\"27\" alt=\"image2.png\"/>\nyou get this for \n<img src=\"https://www.dummies.com/wp-content/uploads/397873.image3.png\" width=\"229\" height=\"100\" alt=\"image3.png\"/>\nwhere A= Ax Ay Az.\nThe part in the parentheses in the exponent is the dot product of the vectors \n<img src=\"https://www.dummies.com/wp-content/uploads/397874.image4.png\" width=\"97\" height=\"19\" alt=\"image4.png\"/>\nThat is, if the vector a = (ax, ay, az) in terms of components and the vector b = (bx, by, bz), then the dot product of a and b is \n<img src=\"https://www.dummies.com/wp-content/uploads/397875.image5.png\" width=\"176\" height=\"29\" alt=\"image5.png\"/>\nSo here’s how you can rewrite the \n<img src=\"https://www.dummies.com/wp-content/uploads/397876.image6.png\" width=\"127\" height=\"63\" alt=\"image6.png\"/>","description":"At some point, your quantum physics instructor may want you to find the x, y, and z equations for three-dimensional free particle problems. Take a look at the x equation for the free particle,\n<img src=\"https://www.dummies.com/wp-content/uploads/397870.image0.png\" width=\"140\" height=\"43\" alt=\"image0.png\"/>\nYou can write its general solution as\n<img src=\"https://www.dummies.com/wp-content/uploads/397871.image1.png\" width=\"456\" height=\"156\" alt=\"image1.png\"/>\nwhere Ay and Az are constants. \nBecause \n<img src=\"https://www.dummies.com/wp-content/uploads/397872.image2.png\" width=\"180\" height=\"27\" alt=\"image2.png\"/>\nyou get this for \n<img src=\"https://www.dummies.com/wp-content/uploads/397873.image3.png\" width=\"229\" height=\"100\" alt=\"image3.png\"/>\nwhere A= Ax Ay Az.\nThe part in the parentheses in the exponent is the dot product of the vectors \n<img src=\"https://www.dummies.com/wp-content/uploads/397874.image4.png\" width=\"97\" height=\"19\" alt=\"image4.png\"/>\nThat is, if the vector a = (ax, ay, az) in terms of components and the vector b = (bx, by, bz), then the dot product of a and b is \n<img src=\"https://www.dummies.com/wp-content/uploads/397875.image5.png\" width=\"176\" height=\"29\" alt=\"image5.png\"/>\nSo here’s how you can rewrite the \n<img src=\"https://www.dummies.com/wp-content/uploads/397876.image6.png\" width=\"127\" height=\"63\" alt=\"image6.png\"/>","blurb":"","authors":[{"authorId":8967,"name":"Steven Holzner","slug":"steven-holzner","description":"Steven Holzner was an award-winning author of more than 130 books, of which more than 2 million copies have been sold. 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Finding the x, y, and z Equations for Three-Dimensional Free Particle Problems

By: Steven Holzner and

Updated: 03-26-2016

From The Book: Quantum Physics For Dummies, Revised Edition

Quantum Physics For Dummies, Revised Edition

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At some point, your quantum physics instructor may want you to find the x, y, and z equations for three-dimensional free particle problems. Take a look at the x equation for the free particle,

You can write its general solution as

where A_y and A_z are constants.

Because

you get this for

where A= A_x A_y A_z.

The part in the parentheses in the exponent is the dot product of the vectors

That is, if the vector a = (a_x, a_y, a_z) in terms of components and the vector b = (b_x, b_y, b_z), then the dot product of a and b is

So here’s how you can rewrite the

About This Article

This article is from the book:

Quantum Physics For Dummies, Revised Edition ,

About the book author:

Steven Holzner is an award-winning author of technical and science books (like Physics For Dummies and Differential Equations For Dummies). He graduated from MIT and did his PhD in physics at Cornell University, where he was on the teaching faculty for 10 years. He’s also been on the faculty of MIT. Steve also teaches corporate groups around the country.

This article can be found in the category:

Quantum Physics ,