# Linked Questions

1answer
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### What is the common difference between partial time derivative and ordinary time derivative? [duplicate]

What is difference between partial and ordinary time derivative? for example: what is difference between $\frac {\partial v}{\partial t}$ and $\frac {dv}{dt}$? where the $v$ is velocity.
3answers
827 views

### Why there is added a partial time derivative in formula for time derivative of potential energy? [duplicate]

In proving the total energy in conservative field is constant we have this equation(picture) why it added partial derivative? Why? I mean where it did come from?
1answer
293 views

### Difference between $dM/dt$ and $\partial M/\partial t$ [duplicate]

$\frac{dM}{dt} = 0$ represents a constant of motion $M.$ Why not $\frac{\partial M}{\partial t}$ represent a constant of motion $M$?
0answers
36 views

I am trying to explain what implicit time dependence is and how it differs from explicit time dependence, but I'm unsure how "sound" my explanation is. Here is what I said: Suppose I have a function $... 2answers 2k views ### Symbols of derivatives What is the exact use of the symbols$\partial$,$\delta$and$\mathrm{d}$in derivatives in physics? How are they different and when are they used? It would be nice to get that settled once and for ... 4answers 1k views ### Hamilton equations from Poisson bracket's formulation Referring to Wikipedia we have that the equation of motion for a$f(q, p, t)$comes from the formula \begin{equation} \frac{\mathrm{d}}{\mathrm{d}t} f(p, q, t) = \frac{\partial f}{\partial q} \frac{\... 5answers 3k views ### Which derivative with respect to time is which in the Heisenberg picture of quantum mechanics? For an observable$A$and a Hamiltonian$H$, Wikipedia gives the time evolution equation for$A(t) = e^{iHt/\hbar} A e^{-iHt/\hbar}$in the Heisenberg picture as $$\frac{d}{dt} A(t) = \frac{i}{\hbar} ... 4answers 3k views ### Conserved quantities and total derivatives? I am having a bit of a crisis in understanding of the physical meanings of total derivatives. When a quantity \rho (be it a vector or a scalar) is said to be conserved, then (mathematically)$$\... 4answers 2k views ### Which Schrödinger equation is correct? In the coordinate representation, in 1D, the wave function depends on space and time,$\Psi(x,t)$, accordingly the time dependent Schrödinger equation is $$H\Psi(x,t) = i\hbar\frac{\partial}{\... 2answers 2k views ### Conserved quantities commute with Hamiltonian — don't understand proof http://en.wikipedia.org/wiki/Constant_of_motion#In_quantum_mechanics I understand the derivation to get$$\frac{d}{dt}⟨\psi|Q|\psi⟩ = -\frac{1}{i\hbar}⟨\psi|[H,Q]\psi⟩ + ⟨\psi|\frac{d}{dt}Q|\psi⟩$$... 3answers 730 views ### Can the kinetic energy be a function of the position vector? ,I got one confusion when reading Goldstein's Classical Mechanics (page 20, third edition). After getting the equation$$ \sum \left\{\left[\frac{\mathrm{d}}{\mathrm{d}t}{\left(\frac{\partial T}{\... 1answer 989 views ### Full time-derivative, Poisson brackets and Hamilton's equations (classical mechanics) While studying Poisson brackets in classical mechanics and the derivation of$\dot{q_j}=\{q_j,H\}$and$\dot{p_j}=\{p_j,H\}$form of Hamilton's equations I encountered a surpsing identity, which led ... 2answers 173 views ### Lagrangian mechanics not relying on time or independent of time [closed] If neither the potential energy nor kinetic energy depends on time, then Lagrangian is explicitly independent of time I find this statement a little bit odd because velocity is distance over time or ... 2answers 316 views ### Principle of least action:$\frac{d S_{cl}}{dt_b} = \frac{\partial S_{cl}}{\partial t_b} + \frac{\partial S_{cl}}{\partial x_b}\dot{x}_b\$

Question I cannot see how I can obtain the yellow highlighted section on the RHS from that of the LHS. The following equation can be found in both my lecture notes(*1) (page 9, equation 2.7) and is ...
1answer
513 views

### Partial derivatives vs total derivatives in thermodynamics

The specific heat of a system is defined as $$C_z = T \left( \frac{\partial S}{\partial T} \right)_{z=\text{const}}$$ Sometimes however, I find the same definition, but with total derivatives ...

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