A finite wave train, of an unspecified nature, propagates along the positive X-axis with a constant speed v and without any change of shape. The differential equation among the four listed below, whose solution it must be, is
A. $$\left( {\frac{{{\partial ^2}}}{{\partial {x^2}}} - \frac{1}{{{v^2}}}\frac{{{\partial ^2}}}{{\partial {t^2}}}} \right)\psi \left( {x,\,t} \right) = 0$$
B. $$\left( {{\nabla ^2} - \frac{1}{{{v^2}}}\frac{{{\partial ^2}}}{{\partial {t^2}}}} \right)\psi \left( {\overrightarrow r ,\,t} \right) = 0$$
C. $$\left( { - \frac{h}{{2m}}\frac{{{\partial ^2}}}{{\partial {x^2}}} - ih\frac{\partial }{{\partial t}}} \right)\psi \left( {x,\,t} \right) = 0$$
D. $$\left( {{\nabla ^2} + a\frac{\partial }{{\partial t}}} \right)\psi \left( {\overrightarrow r ,\,t} \right) = 0$$
Answer: Option A
This Question Belongs to Engineering Physics >> Mathematical Physics
A. $$\frac{{1 + i}}{{\sqrt 2 }}a{\text{ and}} - \frac{{1 + i}}{{\sqrt 2 }}a$$
B. $$ia{\text{ and }} - ia$$
C. $$ia,\, - ia,\,\frac{{1 - i}}{{\sqrt 2 }}a{\text{ and}} - \frac{{1 - i}}{{\sqrt 2 }}a$$
D. $$\frac{{1 + i}}{{\sqrt 2 }}a,\, - \frac{{1 + i}}{{\sqrt 2 }}a,\,\frac{{1 - i}}{{\sqrt 2 }}a{\text{ and}} - \frac{{1 - i}}{{\sqrt 2 }}a$$
Which of the following functions of the complex variable z is not analytic everywhere?
A. ez
B. $$\sin \frac{{\text{z}}}{{\text{z}}}$$
C. e3
D. |z|3
A. \[\left( {1 - \sqrt 3 } \right){{{\bf{\hat i}}}^{\bf{'}}} + 3{{{\bf{\hat j}}}^{\bf{'}}} + \left( {1 + \sqrt 3 } \right){{{\bf{\hat k}}}^{\bf{'}}}\]
B. \[\left( {1 + \sqrt 3 } \right){{{\bf{\hat i}}}^{\bf{'}}} + 3{{{\bf{\hat j}}}^{\bf{'}}} + \left( {1 - \sqrt 3 } \right){{{\bf{\hat k}}}^{\bf{'}}}\]
C. \[\left( {1 - \sqrt 3 } \right){{{\bf{\hat i}}}^{\bf{'}}} + \left( {3 + \sqrt 3 } \right){{{\bf{\hat j}}}^{\bf{'}}} + 2{{{\bf{\hat k}}}^{\bf{'}}}\]
D. \[\left( {1 - \sqrt 3 } \right){{{\bf{\hat i}}}^{\bf{'}}} + \left( {3 - \sqrt 3 } \right){{{\bf{\hat j}}}^{\bf{'}}} + 2{{{\bf{\hat k}}}^{\bf{'}}}\]
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